If \(q\) is the capacitor's charge and \(i\) is the current at time \(t\), the voltage \(V\) will be:
1. | \(L \frac{di}{dt}+{iR}-\frac{q}{C}=V\) |
2. | \(L \frac{di}{dt}-{iR}+\frac{q}{C}=V\) |
3. | \(L \frac{di}{dt}+{iR}+\frac{q}{C}=V\) |
4. | \(L\frac{di}{dt}-{iR}-\frac{q}{C}=V\) |
A direct current of \(5~ A\) is superimposed on an alternating current \(I=10sin ~\omega t\) flowing through a wire. The effective value of the resulting current will be:
1. | \(15/2~A\) | 2. | \(5 \sqrt{3}~A\) |
3. | \(5 \sqrt{5}~A\) | 4. | \(15~A\) |
An \(LCR\) series circuit with \(100~\Omega\) resistance is connected to an AC source of \(200\) V and an angular frequency of \(300\) rad/s. When only the capacitance is removed, the current lags behind the voltage by \(60^{\circ}.\) When only the inductance is removed, the current leads the voltage by \(60^{\circ}.\) Calculate the power dissipated in the \(LCR\) circuit.
1. \(200\) W
2. \(400\) W
3. \(300\) W
4. zero
For which of the following reasons are LC oscillations not sustainable for long?
1. | Every inductor has some resistance. |
2. | The effect of resistance is to introduce a damping effect on the charge & current in the circuit and the oscillations finally die away. |
3. | Even if the resistance is zero, the total energy of the system is radiated away from the system in the form of electromagnetic radiation. |
4. | All of the above |
An ideal resistance \(R\), ideal inductance \(L\), ideal capacitance \(C\), and AC voltmeters \(V_1, V_2, V_3~\text{and}~V_4 \)
1. | Reading in \(V_3\) = Reading in \(V_1\) |
2. | Reading in \(V_1\) = Reading in \(V_2\) |
3. | Reading in \(V_2\) = Reading in \(V_4\) |
4. | Reading in \(V_2\) = Reading in \(V_3\) |
A transistor-oscillator using a resonant circuit with an inductance \(L\) (of negligible resistance) and a capacitance \(C\) has a frequency \(f\). If \(L\) is doubled and \(C\) is changed to \(4C\), the frequency will be:
1. \(\frac{f}{4}\)
2. \(8f\)
3. \(\frac{f}{2\sqrt{2}}\)
4. \(\frac{f}{2}\)
1. | \(50\) V | 2. | \(50 \sqrt{2} ~\text{V}\) |
3. | \(100\) V | 4. | \(0\) V |
An AC ammeter is used to measure the current in a circuit. When a given direct current passes through the circuit, the AC ammeter reads \(6\) A. When another alternating current passes through the circuit, the AC ammeter reads \(8\) A. Then the reading of this ammeter if DC and AC flow through the circuit simultaneously is:
1. \(10 \sqrt{2}\) A
2. \(14\) A
3. \(10\) A
4. \(15\) A
The AC source in the circuit shown in the figure produces a voltage \(V = 20\cos(2000t)\) volts. Neglecting source resistance, the voltmeter and ammeter readings will be (approximately):
1. | \(4~\text{V}, 2.0~\text{A}\) | 2. | \(0~\text{V}, 2~\text{A}\) |
3. | \(5.6~\text{V}, 1.4~\text{A}\) | 4. | \(8~\text{V}, 2.0~\text{A}\) |
In the circuit shown, the AC source has a voltage
\(V= 20\cos(\omega t)\) volts with \(\omega = 2000\) rad/s. The amplitude of the current will be nearest to:
1. \(2\) A
2. \(3.3\) A
3. \(\frac{2}{\sqrt{5}}\) A
4. \(\sqrt{5}\) A