Search any question & find its solution
Question:
Answered & Verified by Expert
A uniform wire of resistance $R$ and length $L$ is cut into four equal parts, each of length $L / 4$ which are then connected in parallel combination. The effective resistance of the combination will be
Options:
Solution:
2356 Upvotes
Verified Answer
The correct answer is:
$\frac{R}{16}$
$\begin{array}{ll}R=\frac{\rho l}{A} \text { or } R \propto l \\ \therefore & \frac{R_1}{R_2}=\frac{I_1}{I_2}=\frac{L}{L / 4}=4 \\ \text { or } & R_2=\frac{R}{4}\left(\because R_1=R\right)\end{array}$
In parallel combination of such four resistance
$\frac{1}{R^{\prime}}=\frac{1}{R_2}+\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_2}$
or $\quad \frac{1}{R^{\prime}}=\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}$
or $\quad \frac{1}{R^{\prime}}=\frac{4}{R}+\frac{4}{R}+\frac{4}{R}+\frac{4}{R}$
or $\quad \frac{1}{R^{\prime}}=\frac{16}{R}$
or $\quad R^{\prime}=R / 16$
In parallel combination of such four resistance
$\frac{1}{R^{\prime}}=\frac{1}{R_2}+\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_2}$
or $\quad \frac{1}{R^{\prime}}=\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}$
or $\quad \frac{1}{R^{\prime}}=\frac{4}{R}+\frac{4}{R}+\frac{4}{R}+\frac{4}{R}$
or $\quad \frac{1}{R^{\prime}}=\frac{16}{R}$
or $\quad R^{\prime}=R / 16$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.