Answer to Question #157106 in Electric Circuits for ABE TEMILOLUWA

Question

the terminal p.d of a battery is 12volts when an external circuit of 20 ohms was connected and 13.5volts when an external resistanceof 45 ohms was connected. calculate the e.m.f and the internal resistance of the battery

Answer 1

We will note the e.m.f. of a battery by $\varepsilon$, it's internal resistance by $r$, the external resistance by $R_1, R_2$ and the terminal p.d. by $V_1, V_2$. Then we have

$V_1 = I_1 R_1 = \frac{\varepsilon}{R_1+r}\cdot R_1$

$V_2 = I_2 R_2 = \frac{\varepsilon}{R_2+r}\cdot R_2$

So we have a system of two linear equations :

$\begin{cases} R_1 \varepsilon - V_1r = R_1 V_1 \\R_2 \varepsilon - V_2 r = R_2 V_2 \end{cases}$

$\begin{cases} 20 \varepsilon - 12r = 240 \\45 \varepsilon - 13.5 r = 607.5 \end{cases}$

By solving this system we get that $\varepsilon = 15V, r=5\Omega$.