A-level Physics (Advancing Physics)/Internal Resistance/Worked Solutions

'''1. A 9V battery is short-circuited. The potential difference across the battery is found to be 8V, and the current is 5A. What is the internal resistance of the battery?'''

8 = 9 - 5Rinternal

5Rinternal = 1

Rinternal = 0.2Ω



2. What is the EMF of the battery in the following circuit?

$$\sum R_{\mathrm{external}} = \left( \frac{1}{8 + 4} + \frac{1}{4} \right)^{-1} = \left( \frac{1}{3} \right)^{-1} = 3 \mbox{ }\Omega$$

Vexternal = 5 x 3 = 15 V

15 = E - (5 x 10)

E = 50 + 15 = 65 V



3. What is the internal resistance of the battery in the following circuit?

$$\sum R_{\mathrm{external}} = \left( \frac{1}{2 + 4} + \frac{1}{3 + 6 + 1} \right)^{-1} = \left( \frac{4}{15} \right)^{-1} = 3.75 \mbox{ }\Omega$$

Vexternal = 7.5 x 3.75 = 28.125

Which actually makes this question impossible because the current is too high for the resistance supplied to the circuit.