Question

(1) A battery of emf 10V and internal resistance 5 ohms is connected to a resistor. If the current in the circuit is 0.5A, what is the resistance of the resistor?
(2) In the above problem, what is the terminal voltage of the battery if the circuit is closed?

Answer 1

$$\begin{gathered} Emf\left(E\right)=10V \\ r=5ohm \\ I=0.5A \\ I=\frac{E}{R+r} \\ 0.5=\frac{10}{R+5} \\ 0.5R+2.5=10 \\ R=15ohm \\ TerminalVoltage\left(V\right)=E-Ir \\ V=10-0.5\times 5 \\ V=7.5V \end{gathered}$$