As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is (√a/π) A. The value of a is

Question

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is (√a/π) A. The value of a is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f =50 Hz X L =2 π fL =2 π(50)(200 × 10-3) =20 π Ω i 0=( V 0/ X L ) ⇒ ( V rms √2/ X L ) =((220) √2/20 π)=(11 √2/π) i o =(√242/π)

Q. As shown in the figure an inductor of inductance $200 m H$ is connected to an $A C$ source of emf $220 V$ and frequency $50 Hz$ . The instantaneous voltage of the source is $0 V$ when the peak value of current is $\frac{a}{π} A$ . The value of a is ____

$f = 50 Hz$
$X_{L} = 2 π f L$
$= 2 π (50) (200 \times 1 0^{- 3})$
$= 20 π Ω$
$i_{0} = \frac{V _{0}}{X _{L}} \Rightarrow \frac{V _{r m s} 2}{X _{L}}$
$= \frac{( 220 ) 2}{20 π} = \frac{11 2}{π}$
$i_{o} = \frac{242}{π}$

Q. As shown in the figure an inductor of inductance 200mH is connected to an AC source of emf 220V and frequency 50Hz. The instantaneous voltage of the source is 0V when the peak value of current is πa​​A. The value of a is ____

f=50Hz XL​=2πfL =2π(50)(200×10−3) =20πΩ i0​=XL​V0​​⇒XL​Vrms​2​​ =20π(220)2​​=π112​​ io​=π242​​

Q. As shown in the figure an inductor of inductance $200 m H$ is connected to an $A C$ source of emf $220 V$ and frequency $50 Hz$ . The instantaneous voltage of the source is $0 V$ when the peak value of current is $\frac{a}{π} A$ . The value of a is ____

$f = 50 Hz$
$X_{L} = 2 π f L$
$= 2 π (50) (200 \times 1 0^{- 3})$
$= 20 π Ω$
$i_{0} = \frac{V _{0}}{X _{L}} \Rightarrow \frac{V _{r m s} 2}{X _{L}}$
$= \frac{( 220 ) 2}{20 π} = \frac{11 2}{π}$
$i_{o} = \frac{242}{π}$