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Q.

In an $L-R$ circuit, the value of $L$ is $(\frac{0.4}{π})$ Henry and the value of $R$ is $30 ohm$ . If in the circuit, an alternating emf of $200 volt$ at 50 cycles per second is connected, the impedance of the circuit and current will be:

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a

11.4 ohm, 17.5 ampere

b

40.4 ohm, 5 ampere

c

50 ohm, 4 ampere

d

30.7 ohm, 6.5 ampere

answer is D.

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Detailed Solution

Here, $X_{L} = ω L = 2 π f L = 2 π \times 50 \times \frac{0.4}{π} = 40 Ω$

$R = 30 Ω$

$∴$ $Z = \sqrt{R^{2} + X_{L}^{2}} = \sqrt{30^{2} + 40^{2}} = 50 Ω$

$I_{r m s} = \frac{V_{r m s}}{Z} = \frac{200}{50} = 4 A$ .

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In an L-R circuit, the value of L is (0.4π) Henry and the value of R is30 ohm . If in the circuit, an alternating emf of 200 volt at 50 cycles per second is connected, the impedance of the circuit and current will be: