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 - 5R_internal

5R_internal = 1

R_internal = 0.2Ω

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

$\sum R_{\mathrm{e}\mathrm{x}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{a}\mathrm{l}}={(\frac{1}{8+4}+\frac{1}{4})}^{-1}={\left(\frac{1}{3}\right)}^{-1}=3\mathrm{\Omega }$

V_external = 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?

$\sum R_{\mathrm{e}\mathrm{x}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{a}\mathrm{l}}={(\frac{1}{2+4}+\frac{1}{3+6+1})}^{-1}={\left(\frac{4}{15}\right)}^{-1}=3.75\mathrm{\Omega }$

V_external = 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.