Question

With a 1600 MΩ resistor across its terminals, the terminal voltage of a certain battery is 2.64 V . With only a 5.12 Ω resistor across its terminals, the terminal voltage is 1.81 V

What would be the terminal voltage if the 5.12 Ω resistor were replaced by a 7.12 Ω resistor?

Find the internal resistance of this battery

Answer 1

If we consider r be the internal resistance and E be the Emf, then,

Using voltage divider

2.64 = 1600 E/(1600 + r)

4224 + 2.64r = 1600 E

1600 E - 2.64r = 4224 ........ (1)

1.81 = 5.12 E/(5.12 + r)

5.12E - 1.81r = 9.27 ........ (2)

So,

Emf, E = 2.64 V

Internal resistance, r = 2.36 ohm

Terminal voltage = (7.12 x 2.64)/(7.12 + 2.36) = 1.98 V

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