Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A lamb in which 10 A current can flow at 15 V is connected with an alternating source of potential 220 V and frequency 50 Hz. What should be the inductance of choke coil required to light the bulb?
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Calculate the resistance of the lamp using Ohm's Law. The current flowing through the lamp is 10 A at 15 V, so the resistance (R) of the lamp can be calculated as follows:
R = \frac{V}{I} = \frac{15 \text{ V}}{10 \text{ A}} = 1.5 \Omega.
Step 2: Calculate the reactance required for the alternating source of 220 V and frequency of 50 Hz. The total impedance (Z) when connected to the 220 V source needs to be calculated to determine the required inductance. We know that:
V = IZ,
where V = 220 V and I = 10 A (the same current).
Therefore,
Z = \frac{V}{I} = \frac{220 \text{ V}}{10 \text{ A}} = 22 \Omega.
Step 3: The impedance in an RL circuit is given by the formula:
Z = \sqrt{R^2 + (XL)^2},
where XL is the inductive reactance given by:
XL = \omega L = 2\pi f L.
Substituting the known values:
22 = \sqrt{(1.5)^2 + (2\pi (50) L)^2}.
Step 4: Squaring both sides:
484 = (1.5)^2 + (314.16 L)^2.
484 = 2.25 + (314.16 L)^2.
Subtract to isolate the inductive part:
481.75 = (314.16 L)^2.
Step 5: Solve for L:
L = \frac{\sqrt{481.75}}{314.16}.
Calculating gives us:
L \approx \frac{21.93}{314.16} \approx 0.0698 ext{ H}.
Therefore, the correct inductance of the choke coil required to light the bulb is approximately 0.0698 H.
R = \frac{V}{I} = \frac{15 \text{ V}}{10 \text{ A}} = 1.5 \Omega.
Step 2: Calculate the reactance required for the alternating source of 220 V and frequency of 50 Hz. The total impedance (Z) when connected to the 220 V source needs to be calculated to determine the required inductance. We know that:
V = IZ,
where V = 220 V and I = 10 A (the same current).
Therefore,
Z = \frac{V}{I} = \frac{220 \text{ V}}{10 \text{ A}} = 22 \Omega.
Step 3: The impedance in an RL circuit is given by the formula:
Z = \sqrt{R^2 + (XL)^2},
where XL is the inductive reactance given by:
XL = \omega L = 2\pi f L.
Substituting the known values:
22 = \sqrt{(1.5)^2 + (2\pi (50) L)^2}.
Step 4: Squaring both sides:
484 = (1.5)^2 + (314.16 L)^2.
484 = 2.25 + (314.16 L)^2.
Subtract to isolate the inductive part:
481.75 = (314.16 L)^2.
Step 5: Solve for L:
L = \frac{\sqrt{481.75}}{314.16}.
Calculating gives us:
L \approx \frac{21.93}{314.16} \approx 0.0698 ext{ H}.
Therefore, the correct inductance of the choke coil required to light the bulb is approximately 0.0698 H.
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