Two wires of the same material having lengths | vedclass

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(B) Since both wires are connected in parallel to the same potential source,the potential difference across each wire is the same.$V_1 = V_2 = 6 \ V$U

Vedclass · Accepted Answer

$3:1$

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(B) Since both wires are connected in parallel to the same potential source,the potential difference across each wire is the same.$V_1 = V_2 = 6 \ V$Using Ohm's Law,$V = IR$,we have $I_1 R_1 = I_2 R_2$,which implies $\frac{I_1}{I_2} = \frac{R_2}{R_1}$.The resistance of a wire is given by $R = ho \frac{l}{A} = ho \frac{l}{\pi r^2}$.Since the material is the same,the resistivity $ho$ is the same for both wires.Thus,$\frac{R_2}{R_1} = \frac{ho \frac{l_2}{\pi r_2^2}}{ho \frac{l_1}{\pi r_1^2}} = \frac{l_2}{l_1} 	imes \left(\frac{r_1}{r_2}ight)^2$.Given $\frac{l_1}{l_2} = \frac{3}{4}$ and $\frac{r_1}{r_2} = \frac{3}{2}$.Substituting these values: $\frac{I_1}{I_2} = \frac{4}{3} 	imes \left(\frac{3}{2}ight)^2 = \frac{4}{3} 	imes \frac{9}{4} = \frac{3}{1}$.Therefore,the ratio $I_1:I_2 = 3:1$.

Two wires of the same material having lengths and radii in the ratio of $3:4$ and $3:2$ respectively are connected in parallel with a potential source of $6 \ V$. The ratio of currents flowing through them $I_1:I_2$ is . . . . . . .

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