Current Electricity 2 Question 10
10. When the switch $S$ in the circuit shown is closed, then the value of current $i$ will be
(2019 Main, 9 Jan I)
(a) $4 A$
(b) $3 A$
(c) $2 A$
(d) $5 A$
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Solution:
- When the switch ’ $S$ ’ is closed the circuit, hence formed is given in the figure below,
Then, according to Kirchhoff’s current law, which states that the sum of all the currents directed towards a point in a circuit is equal to the sum of all the currents directed away from that point.
Since, in the above circuit, that point is ’ $C$ '
$$ \begin{array}{lc} \therefore & i _1+i _2=i \\ \Rightarrow & \frac{V _A-V _C}{2}+\frac{V _B-V _C}{4}=\frac{V _C-V}{2} \\ \text { or } & \frac{20-V _C}{2}+\frac{10-V _C}{4}=\frac{V _C-0}{2} \\ \Rightarrow & 20-V _C+\left(10-V _C\right) 2=V _C \\ & 40=V _C+3 V _C \\ \text { or } \quad 40=4 V _C \\ \therefore \text { The current, } i=\frac{V _C}{2}=\frac{10}{2}=5 A \end{array} $$
