Impedance

Q.

An inductance coil has a reactance of $100\Omega$. When an AC signal of frequency$1000Hz$ is applied to the coil, the applied voltage leads the current by ${45}^0$. The self-inductance of the coil is:

1. $6.7\times {10}^{-7}H$

2. $5.5\times {10}^{-5}H$

3. $1.1\times {10}^{-1}H$

4. $1.1\times {10}^{-2}H$

Q. A series R-C circuit is connected to an alternating voltage source. Consider two situations:
(a) When capacitor is filled with air
(b) When capacitor is filled with mica
Current through resistor is $i$ and voltage across capacitor is $V_a$ in case (a) and $V_b$ in case (b), then

1. $V_a=V_b$
2. $V_a<V_b$
3. $V_a>V_b$
4. $i_a=i_b$

Q. When 100 volts dc is supplied across a solenoid, a current of 1.0 amperes flows in it. When 100 volts ac is applied across the same coil, the current drops to 0.5 ampere. If the frequency of ac source is 50 Hz, then the impedance and inductance of the solenoid are

1. $200\Omega and0.55henry$
2. $100\Omega and0.86henry$
3. $200\Omega and1.0henry$
4. $100\Omega and0.93henry$

Q. A capacitor of $10\mu F$ and an inductor of $1H$ are joined in series. An $AC$ of $50\text{Hz}$ is applied to this combination. What is the impedance of the combination?

1. $\frac{5({\pi }^2-5)}{\pi }\Omega$
2. $\frac{100(10-{\pi }^2)}{\pi }\Omega$
3. $\frac{10({\pi }^2-5)}{\pi }\Omega$
4. $\frac{10(10-{\pi }^2)}{\pi }\Omega$

Q.

When 100 V dc is applied across a solenoid, a current of 1.0 A flows in it. When 100 V ac is applied across the same coil, the current drops to 0.5 A. If the frequency of the ac source is 5o Hz, the impedance and inductance of the solenoid are

1. 200 W and 0.55 H

2. 100 W and 0.86 H

3. 200 W and 1.0 H

4. 100 W and 0.93 H