Answer to Question #120784 in Electric Circuits for Solomon Emmanuel Asuzu

Question

A cell of e.m.f. E and internal resistance r was connected in series with two series
external resistors, A (of 8-ohms) and B (of 2-ohms). A high resistance voltmeter
connected across A was found to read 8 volts. When another resistor C (of 8 ohms) was
connected parallel to A, and then across A and C, the voltmeter read 6 volts.
(i) Draw the circuit diagrams of the two arrangements
(ii) Calculate the internal resistance of the cell
(iii) Calculate the e.m.f. of the cell.

Answer 1

From the figure 1 we can see write that

current*resistance = voltage drop

$\frac{E}{10+2+r}\times10=8\ \\10E-8r=96$ .......(1)

From the figure 2 we can write that

$\frac{E}{4.44+2+r}\times4.44=6$

$4.44E-6r=38.64$ ........(2)

from 1 and 2

we get E =10.9 volts and r=1.6 ohm