Find the potential difference `V_a -V_b` between the points `a` and `b` shown in each part of the figure.

Explanation

(a) `q = q_1 + q_2`
using kirchoff law in 3 and 4
`q_2 / 2 + q_2 / 4 - q_1 /4 = 0`
`rArr 2 q_2 + q_2 - q_1 = 0`
`rArr` 3 q-2 = q_1`
In loop 1234, ` q / 2 + q_1 / 4 -12 = 0`
`rArr 2 q_1 + 2 q_2 + q_1 = 48 `
From equation (ii) and (iii)
` 3.3 q-2 +2 q_2 = 48 `
11 q_2 = 48 :. q_2 = 48 / 11 `
`:. V_a - V_b = q_2 / 4m F = 48 / 44 = 12 / 11`
(b) Let the charge in the loop
` q / 2 + q / 4 - 24 + 12 = 0` (fig)
`3 q / 4 = 12`
`q = 16 columb `
` V_a - V_b = -q / 2 mu`
`= -16 / 2 mu F = -8V` ( c)
`V_A - V_B = 2 - 2 - q / 2 mu F `
In the loop
` 2 + 2 - q / 2 - q / 2 = 0 `
or `q = 4 columb `
`:. V_A - V_B = 2 - 4 / 2 = 2 - 2 = 0 volt.`
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