For the circuit shown, with R1 = 1.0 Ω, R2 = 2.0 Ω, E1 = 2 V and E2 =… | JEE Main 2019 (8 Apr, Shift 1)

Q159JEE Main 2019 · 8 APR · SHIFT 1Medium

Kirchhoff's Laws & Measuring Instruments

For the circuit shown, with R1 = 1.0 $\Omega$ , R2 = 2.0 $\Omega$ , E1 = 2 V and E2 = E3 = 4 V, the potential difference between the points 'a' and 'b' is approximately (in V):

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Answer: (a)

Three branches lie between a and b: ( $E_1 = 2$ , $2R_1 = 2\ \Omega$ ), ( $E_2 = 4$ , $R_2 = 2\ \Omega$ ), ( $E_3 = 4$ , $2R_1 = 2\ \Omega$ ), all with + towards a.
Parallel-cell (Millman) formula: $V_{ab} = \frac{\sum E/r}{\sum 1/r}$
$V_{ab} = \frac{2/2 + 4/2 + 4/2}{1/2 + 1/2 + 1/2} = \frac{5}{1.5} \approx 3.3\text{ V}$
So the answer is (a) 3.3.

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