A virtual current of 4 A and 50 Hz flows in an AC circuit containing a coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V, its inductance will be

Question

A virtual current of 4 A and 50 Hz flows in an AC circuit containing a coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V, its inductance will be (A) (1/3 π) H (B) (1/5 π) H (C) (1/7 π) H (D) (1/9 π) H

Tardigrade Admin · Accepted Answer

R=(P/ir m s2)=(240/16)=15 Ω Z=(V/i)=(100/4)=25 Ω Now, XL=√Z2-R2 =√(25)2-(15)2=20 Ω ∴ 2 π v L=20 ⇒ L=(20/2 π × 50)=(1/5 π) H

Q. A virtual current of $4 A$ and $50 Hz$ flows in an $A C$ circuit containing a coil. The power consumed in the coil is $240 W$ . If the virtual voltage across the coil is $100 V$ , its inductance will be

$\frac{1}{3 π} H$

$\frac{1}{5 π} H$

$\frac{1}{7 π} H$

$\frac{1}{9 π} H$

$R = \frac{P}{i _{r m s}^{2}} = \frac{240}{16} = 15 Ω$
$Z = \frac{V}{i} = \frac{100}{4} = 25 Ω$
Now, $X_{L} = Z^{2} - R^{2}$
$= (25)^{2} - (15)^{2} = 20 Ω$
$∴ 2 π vL = 20$
$\Rightarrow L = \frac{20}{2 π \times 50} = \frac{1}{5 π} H$

Q. A virtual current of 4A and 50Hz flows in an AC circuit containing a coil. The power consumed in the coil is 240W. If the virtual voltage across the coil is 100V, its inductance will be

3π1​H

5π1​H

7π1​H

9π1​H