Question

When a coil is connected across a 20 V dc supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz ac supply, it draws a current of 4 A. The self inductance of the coil is ______ mH.
(Take \(\pi\) = 3)

Answer 1

Correct Answer: 10

Determine the self-inductance \( L \) of the coil through the following steps:
1. DC Analysis:
With a 20 V dc supply, the coil draws 5 A. Ohm's Law (\( V = IR \)) yields the coil's resistance \( R \):
\[ R = \frac{V}{I} = \frac{20\, V}{5\, A} = 4\, \Omega \]
2. AC Analysis:
When connected to a 20 V, 50 Hz ac supply, the coil draws 4 A. The impedance \( Z \) is calculated as:
\[ Z = \frac{V}{I} = \frac{20\, V}{4\, A} = 5\, \Omega \]
The impedance in an inductive ac circuit is given by:
\[ Z = \sqrt{R^2 + (X_L)^2} \] where \( X_L \) is the inductive reactance.
3. Inductive Reactance Calculation:
Rearrange the impedance formula to solve for \( X_L \):
\[ X_L = \sqrt{Z^2 - R^2} = \sqrt{5^2 - 4^2} = \sqrt{25 - 16} = 3\, \Omega \]
Inductive reactance \( X_L \) is also expressed as \( X_L = 2\pi f L \). Solve for \( L \):
\[ 3 = 2 \pi f L \implies L = \frac{3}{2 \times 3 \times 50} = \frac{3}{300} = 0.01 \, \text{H} = 10 \, \text{mH} \]
4. Verification:
The computed self-inductance \( L = 10 \) mH matches the specified range of 10,10.
Therefore, the coil's self-inductance is 10 mH.