Answer to Question #157106 in Electric Circuits for ABE TEMILOLUWA

Question #157106

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


1
Expert's answer
2021-01-21T09:56:19-0500

We will note the e.m.f. of a battery by ε\varepsilon, it's internal resistance by rr, the external resistance by R1,R2R_1, R_2 and the terminal p.d. by V1,V2V_1, V_2. Then we have

V1=I1R1=εR1+rR1V_1 = I_1 R_1 = \frac{\varepsilon}{R_1+r}\cdot R_1

V2=I2R2=εR2+rR2V_2 = I_2 R_2 = \frac{\varepsilon}{R_2+r}\cdot R_2

So we have a system of two linear equations :

{R1εV1r=R1V1R2εV2r=R2V2\begin{cases} R_1 \varepsilon - V_1r = R_1 V_1 \\R_2 \varepsilon - V_2 r = R_2 V_2 \end{cases}

{20ε12r=24045ε13.5r=607.5\begin{cases} 20 \varepsilon - 12r = 240 \\45 \varepsilon - 13.5 r = 607.5 \end{cases}

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


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