Q. No.Given that the current \(i_1=3A \sin \omega t\) and the current \(i_2=4A \cos \omega t,\) what will be the expression for the current \(i_3\)?
1. \(5 A \sin \left(\omega t+53^{\circ}\right) \)
2. \(5 A \sin \left(\omega t+37^{\circ}\right) \)
3. \(5 A \sin \left(\omega t+45^{\circ}\right) \)
4. \( 5 A \sin \left(\omega t+30^{\circ}\right)\)
1. \(5 A \sin \left(\omega t+53^{\circ}\right) \)
2. \(5 A \sin \left(\omega t+37^{\circ}\right) \)
3. \(5 A \sin \left(\omega t+45^{\circ}\right) \)
4. \( 5 A \sin \left(\omega t+30^{\circ}\right)\)
In a box \(Z\) of unknown elements (\(L\) or \(R\) or any other combination), an ac voltage \(E = E_0 \sin(\omega t + \phi)\) is applied and the current in the circuit is found to be \(I = I_0 \sin\left(\omega t + \phi +\frac{\pi}{4}\right)\). The unknown elements in the box could be:
| 1. | Only the capacitor |
| 2. | Inductor and resistor both |
| 3. | Either capacitor, resistor, and an inductor or only capacitor and resistor |
| 4. | Only the resistor |
| Assertion (A): | When a current \(I=(3+4 \sin \omega t)\) flows in a wire, then the reading of a dc ammeter connected in series is \(4\) units. |
| Reason (R): | A dc ammeter measures only the value of the current amplitude. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
1. \(\dfrac{1}{20}~\text{A}\)
2. zero
3. \(\dfrac{1}{10}~\text{A}\)
4. \(\dfrac{1}{5}~\text{A}\)
In an AC circuit, the current is given by; \(i=5\sin\left(100t-\frac{\pi}{2}\right)\) and the AC potential is \(V =200\sin(100 t)~\text V.\) The power consumption is:
1. \(20~\text W\)
2. \(40~\text W\)
3. \(1000~\text W\)
4. zero
1. \( \frac{1}{\sqrt{2}}\left(i_1+i_2\right) \)
2. \( \frac{1}{\sqrt{2}}\left(i_i+i_2\right)^2 \)
3. \( \frac{1}{\sqrt{2}}\left(i_1^2+i_2^2\right)^{1 / 2} \)
4. \( \frac{1}{2}\left(i_1^2+i_2^2\right)^{1 / 2}\)
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 \(6~\text A.\) When another alternating current passes through the circuit, the AC ammeter reads \(8~\text A.\) Then the reading of this ammeter if DC and AC flow through the circuit simultaneously is:
1. \(10 \sqrt{2}~\text A\)
2. \(14~\text A\)
3. \(10~\text A\)
4. \(15~\text A\)
\(1 .\) \(P \left(\frac{R}{Z}\right)^{2}\)
\(2 .\) \(P \sqrt{\frac{R}{Z}}\)
\(3 .\) \(P \left(\frac{R}{Z}\right)\)
\(4 .\) \(P\)
A coil of inductive reactance of \(31~\Omega\) has a resistance of \(8~\Omega\). It is placed in series with a condenser of capacitive reactance \(25~\Omega\). The combination is connected to an AC source of \(110\) V. The power factor of the circuit is:
1. \(0.56\)
2. \(0.64\)
3. \(0.80\)
4. \(0.33\)
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. | \(15~A\) |
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