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Physics M.C.Q (1 Marks)

Alternating Current · Uttarakhand Board (UBSE) STD 12 Science (Uttarakhand - English Medium). 12 questions.

Questions

M.C.Q (1 Marks)

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12 questions · auto-graded multiple-choice test.

MCQ 11 Mark
A constant current of 2.8A exists in a resistor. The rms current is:
  • ✓
    2.8A.
  • B
    About 2A.
  • C
    1.4A.
  • D
    Undefined for a direct current.
Answer
Correct option: A.
2.8A.
A constant current exists in a resistor is rms current it is equal to 2.8Amp.
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MCQ 21 Mark
The AC voltage across a resistance can be measured using:
  • A
    A potentiometer.
  • ✓
    A hot-wire voltmeter.
  • C
    A moving-coil galvanometer.
  • D
    A moving-magnet galvanometer.
Answer
Correct option: B.
A hot-wire voltmeter.
The AC voltae across a resustance can be measured using a hot-wore volmeter.
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MCQ 31 Mark
An $AC$ source is rated $220V, 50Hz$. The average voltage is calculated in a time interval of $0.01s$, It :
  • A
    Must be zero.
  • ✓
    May be zero.
  • C
    Is never zero.
  • D
    Is $\Big(\frac{200}{\sqrt{2}}\Big)\text{V}.$
Answer
Correct option: B.
May be zero.
$\text{V}=\text{V}_0\sin\omega\text{t}$ $\omega=2\pi\text{f}=2\times3.14\times50$
$\omega=314$
$\text{V}_\text{avg}=\frac{\int\limits_0^{0.01}\text{V}\text{dt}}{\int\limits_0^{0.01}\text{dt}}$
$=\text{V}_0\Big(\frac{1\cos\omega\text{t}}{\omega}\Big)_0^{0.01}$
$=\frac{\text{V}_0}{\omega\times0.01}\big(1-\cos\omega(0.1)\big)$
$=\frac{\text{V}_0}{314\times0.01}\big(1-\cos(314\times0.01)\big)$
$=\frac{\text{V}_0}{3.14}\big(1-\cos(314)\big)$
$=\frac{\text{V}_0}{3.14}\big(1-\cos\pi\big)$
$=\frac{2\text{V}_0}{\pi}=140.127\text{volt}$
  1.  

if $\text{V}=\text{V}_0\cos\omega\text{t}$
$\text{V}_\text{avg}=\frac{\int\text{V d}\rho}{\int\text{dt}}=0$
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MCQ 41 Mark
The magnetic field energy in an inductor changes from maximum value to minimum value in 5.0ms when connected to an AC source. The frequency of the source:
  • A
    20Hz.
  • ✓
    50Hz.
  • C
    200Hz.
  • D
    500Hz.
Answer
Correct option: B.
50Hz.
Frequency of the source is remain constant = 50Hz.
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MCQ 51 Mark
An $AC$ source producing emf $\in=\in_{0}\Big[\cos\big(100\pi\text{s}^{-1}\big)\text{t}+\cos\big(500\pi\text{s}^{-1}\big)\text{t}\Big]$ is connected in series with a capacitor and a resistor. The steady-state current in the circuit is found to be $\text{i}=\text{i}_1\cos\Big[\big(100\pi\text{s}^{-1}\big)\text{t}+\phi_1\Big]+\text{i}_2\cos\Big[\big(500\pi\text{s}^{-1}\big)\text{t}+\phi_2\Big].$
  • A
    $i_1  > i_2$
  • B
    $i_1 = i_2$
  • ✓
    $i_1 < i_2$
  • D
    The information is insufficient to find the relation between $i_1$ and $i_2$
Answer
Correct option: C.
$i_1 < i_2$
$\text{Q}=\text{C}\in=\in_{0}\text{C}\Big[\cos\big(100\pi\text{s}^{-1}\big)\text{t}+\cos\big(500\pi\text{s}^{-1}\big)\text{t}\Big]$
$\text{i}=\frac{\text{dQ}}{\text{dt}}$
$\text{Q}=\text{C}\in=\in_{0}\text{C}\Big[\cos\big(100\pi\text{s}^{-1}\big)\text{t}+\cos\big(500\pi\text{s}^{-1}\big)\text{t}\Big]$
$\in_0\text{C}\times100\pi\Big[\sin\big(100\pi\text{s}^{-1}\big)\text{t}\Big]$
$+\in_0\text{C}\times500\pi\Big[\sin\big(500\pi\text{s}^{-1}\big)\text{t}\Big]$
$=100\text{C}\pi\in_0\cos\Big[\big(100\pi\text{s}^{-1}\big)\text{t}+\phi_1\Big]$
$+500\text{C}\pi\in_0\cos\Big[\big(500\pi\text{s}^{-1}\big)\text{t}+\phi_2\Big]$
$\text{i}_1=100\pi\in_0\text{C}$ and $\text{i}_2=500\pi\in_0\text{C}$
$\text{i}_2>\text{i}_1$
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MCQ 61 Mark
A series AC circuit has a resistance of $4\Omega$ and a reactance of $3\Omega.$ The impedance of the circuit is:
  • ✓
    $5\Omega$
  • B
    $7\Omega$
  • C
    $\frac{12}{7}\Omega$
  • D
    $\frac{7}{12}\Omega$
Answer
Correct option: A.
$5\Omega$
$\text{Z}=\sqrt{\text{R}^2+\text{X}^2}$
$\text{R}=4\Omega,\text{X}=3\Omega$
$=\text{Z}=\sqrt{4^2+3^2}=5\Omega$
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MCQ 71 Mark
The peak voltage in a 220V AC source is:
  • A
    220V.
  • B
    About 160V.
  • ✓
    About 310V.
  • D
    440V.
Answer
Correct option: C.
About 310V.
$\text{V}_\text{rms}=220\text{V}$
$\text{V}_\text{p}=\sqrt{2}\times\text{V}_\text{rms}$
$=220\times1.414=311\text{volt}$
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MCQ 81 Mark
Transformers are used:
  • A
    In DC circuits only.
  • ✓
    In AC circuits only.
  • C
    In both DC and AC circuits.
  • D
    Neither in DC nor in AC circuits.
Answer
Correct option: B.
In AC circuits only.
Transformers are used in AC circuits only.
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MCQ 91 Mark
The reactance of a circuit is zero. It is possible that the circuit contains:
  • ✓
    An inductor and a capacitor.
  • B
    An inductor but no capacitor.
  • C
    A capacitor but no inductor.
  • D
    Neither an inductor nor a capacitor.
Answer
Correct option: A.
An inductor and a capacitor.
$\text{X}=0$ (Given)
$\text{X}=\text{X}_\text{L}+\text{X}_\text{C}$
$=\omega\text{L}-\frac{1}{\omega\text{C}}=0$
It is possible that the circuit contains an inductor and a capacitor.
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MCQ 101 Mark
An inductor, a resistance and a capacitor are joined in series with an $AC$ source. As the frequency of the source is slightly increased from a very low value, the reactance:
  • ✓
    Of the inductor increases.
  • B
    Of the resistor increases.
  • C
    Of the capacitor increases.
  • D
    Of the circuit increases.
Answer
Correct option: A.
Of the inductor increases.
$\text{X}_\text{L}=\omega\text{L}$
$\text{X}_\text{C}=\frac{1}{\omega\text{C}}$
If frequency increases that causes $'X_L'$ raction of inductor increases and $'X_C'$ reactance of capacitor decreses.
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MCQ 111 Mark
A capacitor acts as an infinite resistance for:
  • ✓
    DC.
  • B
    AC.
  • C
    DC as well as AC.
  • D
    Neither AC nor DC.
Answer
Correct option: A.
DC.
$\text{X}_\text{C}\frac{1}{\omega\text{C}}=\frac{1}{0\times\text{C}}$ $\bigg\{\text{in}\stackrel{{\text{DC}}}{{\omega = 0 }}\bigg\}$
$=\infty$
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MCQ 121 Mark
An alternating current is given by $\text{i}=\text{i}_1\cos\omega\text{t}+\text{i}_2\sin\omega\text{t}.$ The rms current is given by:
  • A
    $\frac{\text{i}_1+\text{i}_2}{\sqrt{2}}$
  • B
    $\frac{|\text{i}_1+\text{i}_2|}{\sqrt{2}}$
  • ✓
    $\sqrt{\frac{\text{i}_1^2+\text{i}_2^2}{2}}$
  • D
    $\sqrt{\frac{\text{i}_1^2+\text{i}_2^2}{\sqrt{2}}}$
Answer
Correct option: C.
$\sqrt{\frac{\text{i}_1^2+\text{i}_2^2}{2}}$
$\text{i}=\text{i}_1\cos\omega\text{t}+\text{i}_2\sin\omega\text{t}$
$\text{I}_\text{rms}=\frac{\int\limits_0^\text{T}\text{I}^2\text{dt}}{\int\limits_0^\text{T}\text{dt}}$
if $\text{I}=\cos\omega\text{t}$
$\text{I}_\text{rms}^2=\frac{\text{I}_0^2}{2}$
$\text{i}=\text{i}_1\cos\omega\text{t}+\text{i}_2\sin\omega\text{t}$
Than $\text{i}_\text{rms}^2=\frac{\text{i}_1^2}{2}+\frac{\text{i}_2^2}{2}$
$\text{i}_\text{rms}=\sqrt{\frac{\text{i}_1^2+\text{i}_2^2}{2}}$
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