What must be the emf E in the circuit so that the current flowing through the $7 \Omega$ resistor is $1.80\;A$? Each emf source has negligible internal resistance.

From Figure,

Using Kirchhoff's current law at point $E$

$I_1 \; + \; I_2 = 1.8$ .......... (i)

In closed loop AEFDA,

$24 - E = 3\; I_1 - 2\; I_2$

$24 - E = 3 (1.8 - I_2) -  2 \; I_2$

By Solving,

$E = 5\;I_2 + 18.6$ .......... (ii)

Again, from closed loop EBCFE,

$E = 1.8 * 7 + 2 * I_2$

$E = 12.6 + 2\; I_2$ .......... (iii)

Solving equation (ii) and (iii), we get

$I_2 = - 2\;A$

Then, $I_1 = 3.8\; A$

From equation (iii), we get

$E = 12.6 + 2 * (-2) = 8.6\;V$

Return to Main Menu