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Standard XII

Physics

Impedance

When a 100 V ...

Question

When a $100 V DC$ is applied across a solenoid, a current of 1.0 A flows in it. When a $100 V AC$ is applied across the same coil, the current drops to $0.5 A$ . If the frequency of the $A C$ source is $50 Hz$ , the impedance and inductance of the solenoid are

200 Ω

and

0.55 H

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100 Ω

and

0.86 H

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200 Ω

and

1.0 H

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100 Ω

and

0.93 H

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Solution

The correct option is A $200 Ω$ and $0.55 H$
From given, $Z = \frac{V_{r m s}}{I_{r m s}} = \frac{100 V}{0.5 A} = 200 Ω$
Now from DC circuit,
$R = \frac{100 V}{1 A} = 100 Ω$
For detailed solution watch the next video
Now in AC circuit
$Z = \sqrt{R^{2} + X_{L}^{2}}; X_{L} = 2 π f L$
$Z = \sqrt{(100)^{2} + (2 π \times 50 \times L)^{2}}$
$\begin{matrix} (200)^{2} = & (2 π \times 50 \times L)^{2} + (100)^{2} L & = 0.55 H \end{matrix}$

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When a 100 V DC is applied across a solenoid, a current of 1.0 A flows in it. When a 100 V AC is applied across the same coil, the current drops to 0.5 A. If the frequency of the AC source is 50 Hz, the impedance and inductance of the solenoid are

The correct option is A 200 Ω and 0.55 HFrom given, Z=VrmsIrms=100 V0.5 A=200 Ω Now from DC circuit, R=100V1A=100 Ω For detailed solution watch the next video Now in AC circuit Z=√R2+X2L ; XL=2πfL Z=√(100)2+(2π×50×L)2 (200)2=(2π×50×L)2+(100)2L=0.55 H

When a $100 V DC$ is applied across a solenoid, a current of 1.0 A flows in it. When a $100 V AC$ is applied across the same coil, the current drops to $0.5 A$ . If the frequency of the $A C$ source is $50 Hz$ , the impedance and inductance of the solenoid are