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QPages 330-331: Q13: HC Verma: Concepts of Physics - Volume 2 Alternating Current Pages 330-331: Q13 Solution: An electric bulb is designed to consume 55 W when operated at…

An electric bulb is designed to consume 55 W when operated at 110 volts. It is connected to a 220 V, 50 Hz line through a choke coil in series. What should be the inductance of the coil for which the bulb gets correct voltage?

Step-by-Step Verified Solution

**Answer:** L≈1.2 HL \approx 1.2 \, \text{H}. **Step-by-Step Explanation:** For the bulb: R=V2P=110255=220 ΩR = \frac{V^2}{P} = \frac{110^2}{55} = 220 \, \Omega. It needs VR=110 VV_R = 110 \, \text{V}. Supply is 220 V rms, so voltage across choke VL=2202−1102=1103 VV_L = \sqrt{220^2 - 110^2} = 110\sqrt{3} \, \text{V}. Current I=110220=0.5 AI = \frac{110}{220} = 0.5 \, \text{A}. XL=VLI=11030.5=2203≈381 ΩX_L = \frac{V_L}{I} = \frac{110\sqrt{3}}{0.5} = 220\sqrt{3} \approx 381 \, \Omega. L=XLω=381100π≈1.2 HL = \frac{X_L}{\omega} = \frac{381}{100\pi} \approx 1.2 \, \text{H} [citation:4].

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