Problem

A battery has an e.m.f. of $12.8 \, \mathrm{V}$ and supplies a current of $3.2 \, \mathrm{A}$.
(a) What is the resistance in the circuit?
(b) How many coulombs leave the battery in 5 minutes?

Data

• Voltage: $V = 12.8 \, \mathrm{V}$
• Current: $I = 3.2 \, \mathrm{A}$
• Time: $t = 5 \, \mathrm{minutes} = 5 \times 60 = 300 \, \mathrm{s}$

Prerequisite Concepts

1. Ohm’s Law:
   $R = \frac{V}{I}$
2. Definition of Current:
   $I = \frac{\Delta Q}{\Delta t} \implies \Delta Q = I \cdot \Delta t$

Solution

(a) Resistance:

$$R = \frac{V}{I} = \frac{12.8}{3.2} = 4 \, \Omega$$

(b) Charge:

$$\Delta Q = I \cdot \Delta t = 3.2 \cdot 300 = 960 \, \mathrm{C}$$

Answer

• Resistance: $R = 4 \, \Omega$
• Charge: $\Delta Q = 960 \, \mathrm{C}$

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