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15/09/2021 11:19 am
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Three resistors having resistances r1, r2 and r3 are connected as shown in the given circuit. The ratio i3/i1 of currents in terms of resistances used in the circuit is :
(1) \(\frac{r_1}{r_2 + r_3}\)
(2) \(\frac{r_2}{r_2 + r_3}\)
(3) \(\frac{r_1}{r_3 + r_2}\)
(4) \(\frac{r_2}{r_1 + r_3}\)
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15/09/2021 11:28 am
Correct answer: (2) \(\frac{r_2}{r_2 + r_3}\)
Explanation:
V = ir
i = \(\frac{V}{r}\)
i ∝ \(\frac{1}{r}\)[v is same for r2 & r3]
\(\frac{i_2}{i_3}\) = \(\frac{r_3}{r_2}\)
i3 = \(\frac{r_2}{r_2 + r_3}i_1\)
\(\frac{i_3}{i_1}\) = \(\frac{r_2}{r_2 + r_3}\)