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A car battery of emf 12 V and internal resistance 0.5 is being charged by a 20 V ideal DC supply. To limit the charging current to 4 A , an external resistor is connected in series with the battery. What should be the value of this external resistor?

Options

  1. A7.5
  2. B2.0
  3. C1.5
  4. D4.5

Correct answer

C. 1.5

Step-by-step solution

During charging, the positive terminal of the DC supply is connected to the positive terminal of the battery. Thus, the two emfs oppose each other. Net emf in the circuit, E_ net = 20 V - 12 V = 8 V . Total resistance in the circuit is the sum of the external resistance R and the internal resistance r of the battery: R_ total = R + 0.5 . According to Ohm's law, the charging current is: I = E_ net R_ total 4 = 8 R + 0.5 R + 0.5 = 2 R = 1.5 . Answer: 1.5

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