Ecrit par ✅ Quiz : Courants Variables
Ce quiz contient 20 questions.
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{
"quiz_title": "Courants Variables",
"quiz_slug": "10_courants_variables_quiz",
"quiz_description": "Quiz Edu509 : Courants Variables",
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"questions": [
{
"question_order": 1,
"question_title": "Dans un circuit à courant alternatif, l’intensité instantanée est donnée par \\\\( i(t) = 3,0 \\\\sin(200 t) \\\\) (en ampères, \\\\( t \\\\) en secondes). Quelle est la valeur maximale du courant \\\\( I_m \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
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"show_question_mark": true,
"question_description": "",
"question_explanation": "La valeur maximale du courant est le coefficient devant le sinus, soit \\\\( I_m = 3,0 \\\\) A.",
"answers": [
{
"answer_title": "3,0 A",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "200 A",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,015 A",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "600 A",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Un générateur fournit une tension alternative de fréquence \\\\( 60 \\\\) Hz. Quelle est la pulsation \\\\( \\\\omega \\\\) correspondante ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation est \\\\( \\\\omega = 2\\\\pi f = 2\\\\pi \\\\times 60 = 377 \\\\) rad/s.",
"answers": [
{
"answer_title": "377 rad/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "120 rad/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "60 rad/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "188 rad/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "Dans un circuit RC, on a \\\\( R = 2{,}0\\\\ \\\\mathrm{k\\\\Omega} \\\\) et \\\\( C = 2{,}5\\\\ \\\\mu\\\\mathrm{F} \\\\). Quel est le temps caractéristique \\\\( \\\\tau \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps caractéristique est \\\\( \\\\tau = RC = 2000 \\\\times 2,5 \\\\times 10^{-6} = 5,0 \\\\times 10^{-3} \\\\) s = 5,0 ms.",
"answers": [
{
"answer_title": "5,0 ms",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,5 ms",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "8,0 ms",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "12,5 ms",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Deux condensateurs de \\\\( 3,0\\\\ \\\\mu\\\\mathrm{F} \\\\) et \\\\( 6,0\\\\ \\\\mu\\\\mathrm{F} \\\\) sont associés en parallèle. Quelle est la capacité équivalente ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "En parallèle, les capacités s’additionnent : \\\\( C_{eq} = 3,0 + 6,0 = 9,0\\\\ \\\\mu\\\\mathrm{F} \\\\).",
"answers": [
{
"answer_title": "9,0 \\\\( \\\\mu\\\\mathrm{F} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2,0 \\\\( \\\\mu\\\\mathrm{F} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "4,5 \\\\( \\\\mu\\\\mathrm{F} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "18,0 \\\\( \\\\mu\\\\mathrm{F} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Dans un circuit RL, \\\\( L = 0,10\\\\ \\\\mathrm{H} \\\\) et \\\\( R = 500\\\\ \\\\Omega \\\\). Quel est le temps caractéristique \\\\( \\\\tau \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps caractéristique est \\\\( \\\\tau = \\\\frac{L}{R} = \\\\frac{0,10}{500} = 0,0002 \\\\) s = 0,20 ms.",
"answers": [
{
"answer_title": "0,20 ms",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,0002 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,0005 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,50 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Un condensateur de \\\\( 8,0\\\\ \\\\mu\\\\mathrm{F} \\\\) est chargé sous une tension de \\\\( 10\\\\ \\\\mathrm{V} \\\\). Quelle est la charge stockée ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La charge est \\\\( q = C \\\\cdot u = 8,0 \\\\times 10^{-6} \\\\times 10 = 80 \\\\times 10^{-6} \\\\) C = 80 \\\\( \\\\mu\\\\mathrm{C} \\\\).",
"answers": [
{
"answer_title": "80 \\\\( \\\\mu\\\\mathrm{C} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "1,25 \\\\( \\\\mu\\\\mathrm{C} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,8 \\\\( \\\\mu\\\\mathrm{C} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "18 \\\\( \\\\mu\\\\mathrm{C} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Dans un circuit, le flux magnétique varie de \\\\( 0,04\\\\ \\\\mathrm{Wb} \\\\) à \\\\( 0,00\\\\ \\\\mathrm{Wb} \\\\) en \\\\( 0,01\\\\ \\\\mathrm{s} \\\\). Quelle est la force électromotrice induite moyenne ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La f.e.m. moyenne est \\\\( e = -\\\\frac{\\\\Delta \\\\Phi}{\\\\Delta t} = -\\\\frac{0,00 - 0,04}{0,01} = 4,0 \\\\) V.",
"answers": [
{
"answer_title": "4,0 V",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,4 V",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "40 V",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,04 V",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Dans un circuit sinusoïdal, \\\\( i(t) = 5,0 \\\\sin(100\\\\pi t) \\\\). Quelle est la fréquence \\\\( f \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation \\\\( \\\\omega = 100\\\\pi \\\\), donc \\\\( f = \\\\frac{\\\\omega}{2\\\\pi} = \\\\frac{100\\\\pi}{2\\\\pi} = 50 \\\\) Hz.",
"answers": [
{
"answer_title": "50 Hz",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "100 Hz",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "5,0 Hz",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "314 Hz",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Une bobine d’inductance \\\\( 0,50\\\\ \\\\mathrm{H} \\\\) est parcourue par un courant \\\\( i(t) = 2,0 \\\\sin(50 t) \\\\). Quelle est la tension instantanée aux bornes de la bobine à \\\\( t = 0 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La dérivée du courant est \\\\( 2,0 \\\\times 50 \\\\cos(50 t) \\\\). À \\\\( t = 0 \\\\), \\\\( \\\\cos(0) = 1 \\\\), donc \\\\( \\\\frac{di}{dt} = 100 \\\\). La tension est \\\\( e_L = -0,50 \\\\times 100 = -50,0 \\\\) V.",
"answers": [
{
"answer_title": "50,0 V",
"is_correct": false,
"answer_order": 1
},
{
"answer_title": "0 V",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "-50,0 V",
"is_correct": true,
"answer_order": 3
},
{
"answer_title": "100 V",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Dans un circuit RC, la tension initiale aux bornes du condensateur est \\\\( 12\\\\ \\\\mathrm{V} \\\\). Après un temps égal au temps caractéristique, quelle est la tension restante lors de la décharge ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Après un temps \\\\( \\\\tau \\\\), \\\\( u_C = U_0 e^{-1} = 12 \\\\times 0,368 = 4,42 \\\\) V.",
"answers": [
{
"answer_title": "4,42 V",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "7,58 V",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "12,0 V",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0 V",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Un circuit RLC série contient \\\\( R = 100\\\\ \\\\Omega \\\\), \\\\( L = 0,20\\\\ \\\\mathrm{H} \\\\), \\\\( C = 10\\\\ \\\\mu\\\\mathrm{F} \\\\). Quelle est la pulsation propre \\\\( \\\\omega_0 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation propre est \\\\( \\\\omega_0 = \\\\frac{1}{\\\\sqrt{LC}} = \\\\frac{1}{\\\\sqrt{0,20 \\\\times 10 \\\\times 10^{-6}}} = \\\\frac{1}{\\\\sqrt{2 \\\\times 10^{-6}}} = \\\\frac{1}{1,414 \\\\times 10^{-3}} = 707 \\\\) rad/s.",
"answers": [
{
"answer_title": "707 rad/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "500 rad/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "1000 rad/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "1414 rad/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Dans un circuit RC, \\\\( R = 1,0\\\\ \\\\mathrm{k\\\\Omega} \\\\), \\\\( C = 10\\\\ \\\\mu\\\\mathrm{F} \\\\), \\\\( U_0 = 5,0\\\\ \\\\mathrm{V} \\\\). Quelle est la tension aux bornes du condensateur après \\\\( 20\\\\ \\\\mathrm{ms} \\\\) lors de la charge ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps caractéristique est \\\\( \\\\tau = 1,0 \\\\times 10^{-2} = 10 \\\\) ms. \\\\( t = 20 \\\\) ms = 2\\\\( \\\\tau \\\\). \\\\( u_C = 5,0 \\\\times (1 - e^{-2}) = 5,0 \\\\times (1 - 0,135) = 5,0 \\\\times 0,865 = 4,32 \\\\) V.",
"answers": [
{
"answer_title": "4,32 V",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2,50 V",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "5,00 V",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "3,16 V",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Un courant alternatif a pour expression \\\\( i(t) = 6,0 \\\\sin(314 t) \\\\). Quelle est la période \\\\( T \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation \\\\( \\\\omega = 314 \\\\), donc \\\\( f = \\\\frac{314}{2\\\\pi} = 50 \\\\) Hz, donc \\\\( T = \\\\frac{1}{50} = 0,02 \\\\) s.",
"answers": [
{
"answer_title": "0,02 s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,314 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,005 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,10 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Dans un circuit RL, \\\\( L = 0,40\\\\ \\\\mathrm{H} \\\\), \\\\( R = 2,0\\\\ \\\\Omega \\\\). Quel est le temps caractéristique \\\\( \\\\tau \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps caractéristique est \\\\( \\\\tau = \\\\frac{L}{R} = \\\\frac{0,40}{2,0} = 0,20 \\\\) s.",
"answers": [
{
"answer_title": "0,20 s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,80 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "2,0 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,02 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Un condensateur de \\\\( 5,0\\\\ \\\\mu\\\\mathrm{F} \\\\) et un autre de \\\\( 15,0\\\\ \\\\mu\\\\mathrm{F} \\\\) sont associés en série. Quelle est la capacité équivalente ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "En série, \\\\( \\\\frac{1}{C_{eq}} = \\\\frac{1}{5,0} + \\\\frac{1}{15,0} = \\\\frac{3 + 1}{15} = \\\\frac{4}{15} \\\\), donc \\\\( C_{eq} = \\\\frac{15}{4} = 3,75 \\\\) \\\\( \\\\mu\\\\mathrm{F} \\\\).",
"answers": [
{
"answer_title": "3,75 \\\\( \\\\mu\\\\mathrm{F} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "20,0 \\\\( \\\\mu\\\\mathrm{F} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "10,0 \\\\( \\\\mu\\\\mathrm{F} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "7,5 \\\\( \\\\mu\\\\mathrm{F} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Dans un circuit RC, \\\\( R = 500\\\\ \\\\Omega \\\\), \\\\( C = 4,0\\\\ \\\\mu\\\\mathrm{F} \\\\). Quel est le temps caractéristique \\\\( \\\\tau \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps caractéristique est \\\\( \\\\tau = 500 \\\\times 4,0 \\\\times 10^{-6} = 2,0 \\\\times 10^{-3} \\\\) s = 2,0 ms.",
"answers": [
{
"answer_title": "2,0 ms",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,2 ms",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "8,0 ms",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "1,0 ms",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Une bobine de \\\\( 0,30\\\\ \\\\mathrm{H} \\\\) est parcourue par un courant \\\\( i(t) = 3,0 \\\\sin(200 t) \\\\). Quelle est la tension instantanée aux bornes de la bobine à \\\\( t = 0 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La dérivée du courant est \\\\( 3,0 \\\\times 200 \\\\cos(200 t) \\\\). À \\\\( t = 0 \\\\), \\\\( \\\\cos(0) = 1 \\\\), donc \\\\( \\\\frac{di}{dt} = 600 \\\\). La tension est \\\\( e_L = -0,30 \\\\times 600 = -180 \\\\) V.",
"answers": [
{
"answer_title": "180 V",
"is_correct": false,
"answer_order": 1
},
{
"answer_title": "0 V",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "-180 V",
"is_correct": true,
"answer_order": 3
},
{
"answer_title": "60 V",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Dans un circuit RC, la tension initiale est \\\\( 10,0\\\\ \\\\mathrm{V} \\\\). Après un temps égal à deux fois le temps caractéristique, quelle est la tension restante lors de la décharge ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Après \\\\( 2\\\\tau \\\\), \\\\( u_C = U_0 e^{-2} = 10,0 \\\\times 0,135 = 1,35 \\\\) V.",
"answers": [
{
"answer_title": "1,35 V",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "3,68 V",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "6,32 V",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "8,65 V",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Dans un circuit à courant alternatif, la tension instantanée est \\\\( u(t) = 220 \\\\sin(314 t) \\\\). Quelle est la valeur efficace de la tension ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La valeur efficace est \\\\( U_{eff} = \\\\frac{U_m}{\\\\sqrt{2}} = \\\\frac{220}{1,414} = 155,6 \\\\) V.",
"answers": [
{
"answer_title": "155,6 V",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "220 V",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "110 V",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "314 V",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Un circuit RC a \\\\( R = 2,0\\\\ \\\\mathrm{k\\\\Omega} \\\\), \\\\( C = 1,0\\\\ \\\\mu\\\\mathrm{F} \\\\). Quel est le temps caractéristique \\\\( \\\\tau \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps caractéristique est \\\\( \\\\tau = 2000 \\\\times 1,0 \\\\times 10^{-6} = 2,0 \\\\times 10^{-3} \\\\) s = 2,0 ms.",
"answers": [
{
"answer_title": "2,0 ms",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,5 ms",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "1,0 ms",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "20 ms",
"is_correct": false,
"answer_order": 4
}
]
}
]
}