Q. No.The electric current in the circuit is given as \(i=i_0 (t/T)\). The r.m.s current for the period \(t=0 \) to \(t =T\) is:
1. \(\dfrac{i_0}{\sqrt{2}}\)
2. \(i_0\)
3. \(\dfrac{i_0}{\sqrt{6}}\)
4. \(\dfrac{i_0}{\sqrt{3}}\)
1. \(\dfrac{i_0}{\sqrt{2}}\)
2. \(i_0\)
3. \(\dfrac{i_0}{\sqrt{6}}\)
4. \(\dfrac{i_0}{\sqrt{3}}\)
Subtopic: RMS & Average Values |
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An alternating current is represented by the equation, \(I=100\sqrt{2} ~\sin(100\pi t) \) ampere. The \(\text{RMS}\) value of current and the frequency of the given alternating current are:
1. \(100 ~\text A, 50~\text{Hz}\)
2. \(100\sqrt{2}~ \text A, 100\text{ Hz}\)
3. \(100/\sqrt{2}~ \text A, 100\text{ Hz}\)
4. \(50\sqrt{2}~\text A, 50\text{ Hz}\)
1. \(100 ~\text A, 50~\text{Hz}\)
2. \(100\sqrt{2}~ \text A, 100\text{ Hz}\)
3. \(100/\sqrt{2}~ \text A, 100\text{ Hz}\)
4. \(50\sqrt{2}~\text A, 50\text{ Hz}\)
Subtopic: RMS & Average Values |
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Level 1: 80%+
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An electric bulb rated as \(100~\text{W}\text-220 ~\text{V}\) is connected to an ac source of rms voltage \(220 ~\text{V}.\) The peak value of current through the bulb is:
1. \(0.45~\text{A}\)
2. \(0.32~\text{A}\)
3. \(0.64~\text{A}\)
4. \(2.2~\text{A}\)
1. \(0.45~\text{A}\)
2. \(0.32~\text{A}\)
3. \(0.64~\text{A}\)
4. \(2.2~\text{A}\)
Subtopic: RMS & Average Values |
62%
Level 2: 60%+
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An ac current is represented as \(i=5√2+10\cos(650πt + π/6) ~\text{A.}\) The rms value of the current is:
1. \(10 ~\text{A}\)
2. \(5\sqrt{2} ~\text{A}\)
3. \(50 ~\text{A}\)
4. \(100 ~\text{A}\)
1. \(10 ~\text{A}\)
2. \(5\sqrt{2} ~\text{A}\)
3. \(50 ~\text{A}\)
4. \(100 ~\text{A}\)
Subtopic: RMS & Average Values |
72%
Level 2: 60%+
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An alternating current is given by \(I = I_A \sin \omega t + I_B \cos \omega t\). The \(rms\) current will be:
1. \(\dfrac{\sqrt{I_A^2+I_B^2}}{2} \)
2. \(\dfrac{\left|I_A+I_B\right|}{\sqrt{2}} \)
3. \(\sqrt{I_A^2+I_B^2}\)
4. \(\sqrt{\dfrac{I_A^2+I_B^2}{2}}\)
1. \(\dfrac{\sqrt{I_A^2+I_B^2}}{2} \)
2. \(\dfrac{\left|I_A+I_B\right|}{\sqrt{2}} \)
3. \(\sqrt{I_A^2+I_B^2}\)
4. \(\sqrt{\dfrac{I_A^2+I_B^2}{2}}\)
Subtopic: RMS & Average Values |
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Level 1: 80%+
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A capacitive AC circuit is given. The RMS value of the current is:
1. \(22~\text{mA}\)
2. \(28~\text{mA}\)
3. \(44~\text{mA}\)
4. \(48~\text{mA}\)
1. \(22~\text{mA}\)
2. \(28~\text{mA}\)
3. \(44~\text{mA}\)
4. \(48~\text{mA}\)
Subtopic: RMS & Average Values |
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Level 1: 80%+
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Instantaneous current in a circuit is \(i(t)=\left[6+\sqrt{54} \sin \left(2 \pi t+\frac{\pi}{3}\right)\right] \mathrm{A}. \)The RMS value of the current is:
1. \(2 \sqrt 6 ~\text A \)
2. \(7~\text A\)
3. \(3 \sqrt 7 ~\text A \)
4. \(6 \sqrt 2 ~\text A \)
1. \(2 \sqrt 6 ~\text A \)
2. \(7~\text A\)
3. \(3 \sqrt 7 ~\text A \)
4. \(6 \sqrt 2 ~\text A \)
Subtopic: RMS & Average Values |
82%
Level 1: 80%+
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For the given figures, choose the correct options:
| 1. | The RMS current in \(\mathrm{figure (a)}\) is always equal to that in \(\mathrm{figure (b)}\) |
| 2. | At resonance, the current in \(\mathrm{(b)}\) is less than that in \(\mathrm{(a)}\) |
| 3. | The RMS current in the circuit \(\mathrm{(b)}\) can never be larger than that in \(\mathrm{(a)}\) |
| 4. | The RMS current in the circuit \(\mathrm{(b)}\) can be larger than that in \(\mathrm{(a)}\) |
Subtopic: RMS & Average Values |
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In a series \(RLC\) circuit, \(R=80~\Omega\), \(X_L=100~\Omega\), \(X_C=40~\Omega\). If the source voltage is \(2500 \cos (628 t)\) V, the peak current is equal to:
1. \(5\) A
2. \(25 \) A
3. \(10\) A
4. \(12\) A
1. \(5\) A
2. \(25 \) A
3. \(10\) A
4. \(12\) A
Subtopic: RMS & Average Values |
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In the AC circuit shown in the figure, the value of \(I_{rms}\) is equal to:
1. \(2\) A
2. \(2\sqrt{2}\) A
3. \(4\) A
4. \(\sqrt{2}\) A
1. \(2\) A
2. \(2\sqrt{2}\) A
3. \(4\) A
4. \(\sqrt{2}\) A
Subtopic: RMS & Average Values |
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Level 1: 80%+
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