Question

Two electric circuits `I and II` are shown in (Fig. 3.55). In circuit `I`, the key `K` is closed whereas in circuit `II`, the key is open. Compare the currents `I` and circuit `II`.
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Answer 1

In circuit `I`, since `K` is closed, `R_1 and R_2` are in parallel combination. Their equivalent resistance is given by
`R_p = (R_1 R_2)/((R_1 + R_2))`
Current in the circuit, `I_1 = (V)/(R_p) = (V(R_1 + R_2))/(R_1 R_2)`
In circuit `II`, since `K` is open, the resistance `R_2` is out of circuit and as such the net resistance in the circuit is `R_1`.
Current in the circuit, `I_2 = (V)/(R_1)`. Thus, `(I_1)/(I_2) = (V(R_1 + R_2))/(R_1 R_2) xx (R_1)/(V) = ((R_1 + R_2))/(R_2)`
since `(R_1 + R_2) gt R_2, I_1 gt I_2`.
Thus, current in circuit `I` is more than the current in circuit `II`.