Question

Find the potential difference Va – Vb in the circuits shown in the figure (32-E12).
figure 32-12

Answer 1

Explanation:

(a) In loop 1, when KVL is applied, we obtain:

i1R2 - E2 + i2R3 + i1 = R3i2 + 0(R2+R3)i1 = E2    …(1)

In loop 2, when KVL is applied, we obtain:

i2R1 + i1 - E1 + i2R3 = R3i2 + 0R1 + R3i1 = E1    … (2)

When equation (1) is multiplied by (R1+R3) and when equation (2) is multiplied by R3 and when (2) is subtracted from (1), we obtain:

i1 = E2R1 + R2R3 - E1R3R1R2 + R3 + R3R1

Likewise, when equation (1) is multiplied by R3 and (2) is multiplied by (R1+R3), and when (2) is subtracted from (1), we obtain:

i2 = - E2R3R1R2 + R3 + R2R3 + R3R1 + E1R2

According to the figure,

Va-Vb = i1 + i2R3  

Va – Vb = E1R1 + 1R2 + 1R3 + E2R21R1

(b) In figure b, the circuit can be redrawn as indicated below:

It can be observed that it is identical to the circuit shown in figure a. So, the answer will be the same.