Current Electricity 2 Question 4
4. For the circuit shown with $R _1=1.0 \Omega, R _2=2.0 \Omega, E _1=2 V$ and $E _2=E _3=4 V$, the potential difference between the points $a$ and $b$ is approximately (in volt) (2019 Main, 8 April I)
(a) 2.7
(b) 2.3
(c) 3.7
(d) 3.3
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Solution:
- Given circuit is
Above circuit can be viewed as
This is a parallel combination of three cells or in other words, a parallel grouping of three cells with internal resistances.
So, $\quad V _{a b}=E _{eq}=\frac{I _{eq}}{r _{eq}}=\frac{\frac{E _1}{r _1}+\frac{E _2}{r _2}+\frac{E _3}{r _3}}{\frac{1}{r _1}+\frac{1}{r _2}+\frac{1}{r _3}}$
$$ =\frac{\frac{2}{2}+\frac{4}{2}+\frac{4}{2}}{\frac{1}{2}+\frac{1}{2}+\frac{1}{2}}=\frac{10}{3} V \approx 3.3 V $$
