Question 37: Current Electricity

Question

Across the 220 V source of internal resistance $20 \Omega$, how many lamps of $40 \mathrm{~W}, 100 \mathrm{~V}$ can be connected in parallel so that all the lamps may glow with full brightness.

Accepted Answer

First, letÃ¢ÂÂs find the total current the source must supply so that its terminal voltage is 100 V:
Source emf $E=220$ V, internal resistance $r=20$\,ÃÂ©, desired terminal voltage $V_L=100$ V.
By KirchhoffÃ¢ÂÂs loop law:
$$V_L = E - I\,r \quad\Longrightarrow\quad I = \frac{E - V_L}{r} = \frac{220 - 100}{20} = 6	ext{ A}.$$
Next, each lamp (40 W at 100 V) draws
$$I_{m lamp} = \frac{P}{V} = \frac{40}{100} = 0.4	ext{ A}.$$
Hence the number of lamps $N$ is
$$N = \frac{I}{I_{m lamp}} = \frac{6}{0.4} = 15.$$
Answer: 15 (Option B).

Answer

40

Answer

15

Answer

30

Answer

20

Current Electricity

Across the 220 V source of internal resistance 20 \Omega, how many lamps of 40 \mathrm{~W}, 100 \mathrm{~V} can be connected in parallel so that all the lamps may glow with full brightness.

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