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 = 0.2

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

$\sum R_{external}=\frac{1}{8+4}+\frac{1}{4}=\frac{1}{3}\mathrm{\Omega }$

V_external = 5 x 0.333 = 1.667 V

1.667 = E - (5 x 10)

E = 50 + 1.667 = 51.667 V

Oh dear, UQS (Unrealistic Question Syndrome) must have hit again...

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

$\sum R_{external}=\frac{1}{2+4}+\frac{1}{3+6+1}=\frac{4}{15}\mathrm{\Omega }\approx 0.267\mathrm{\Omega }$

V_external = 7.5 x 0.267 = 2V

2 = 5 - 7.5R_internal

7.5R_internal = 3

R_internal = 0.4 Ω