First slide

Ohm's law

Question

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of (4/3) and (2/3), then the ratio of the currents passing through the wires will be

NA

A

3
B

1/3
C

8/9
D

2

Solution

See. fig
From figure $V_{A} - V_{B} = i_{1} R_{1} = i_{2} R_{2}$
$∴ \frac{i_{1}}{i_{2}} = \frac{R_{2}}{R_{1}}$ ……………..(1)
We know that $R = ρ (l / {πr}^{2}) or R \propto (l / r^{2})$
So, $\frac{R_{2}}{R_{1}} = \frac{l_{2}}{l_{1}} \times (\frac{r_{1}^{2}}{r_{2}^{2}})$
Given that $\frac{l_{1}}{l_{2}} = \frac{4}{3} and \frac{r_{1}}{r_{2}} = \frac{2}{3}$
$∴ \frac{R_{2}}{R_{1}} = \frac{3}{4} \times {(\frac{2}{3})}^{2} = \frac{1}{3}$ ………………(2)
From eqs. (1) 8nd (2), we get
$\frac{i_{1}}{i_{2}} = \frac{1}{3}$

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