An inductive coil has a resistance of 100 Ω When an AC signal of frequency 1000 Hz is applied to the coil, the voltage leads the current by 45° . The inductance of the coil is

Question

An inductive coil has a resistance of 100 Ω When an AC signal of frequency 1000 Hz is applied to the coil, the voltage leads the current by 45° . The inductance of the coil is (A)  (1/10π )  (B)  (1/20π )  (C)  (1/40π )  (D)  (1/60π )

Tardigrade Admin · Accepted Answer

tan φ=(XL/R) ∴ tan 45o=(L ω/R) L=(R/ω)=(100/2 π × 1000) (∵ tan 45°=1) L=(1/20 π)

Q. An inductive coil has a resistance of $100 Ω$ When an AC signal of frequency $1000 Hz$ is applied to the coil, the voltage leads the current by $4 5^{\circ}$ . The inductance of the coil is

$\frac{1}{10 π}$

$\frac{1}{20 π}$

$\frac{1}{40 π}$

$\frac{1}{60 π}$

$tan ϕ = \frac{X _{L}}{R}$
$∴ tan 4 5^{o} = \frac{L ω}{R}$
$L = \frac{R}{ω} = \frac{100}{2 π \times 1000}$
$(∵ tan 4 5^{\circ} = 1)$
$L = \frac{1}{20 π}$

Q. An inductive coil has a resistance of 100Ω When an AC signal of frequency 1000Hz is applied to the coil, the voltage leads the current by 45∘ . The inductance of the coil is

10π1​

20π1​

40π1​

60π1​