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:
1526 Upvotes
Verified Answer
The correct answer is:
$\frac{R}{16}$
$\begin{aligned}
& R=\frac{\rho l}{A} \text { or } R \propto l \\
& \therefore \quad \frac{R_1}{R_2}=\frac{l_1}{l_2}=\frac{L}{L / 4}=4 \\
& \text { or } \quad R_2=\frac{R}{4} \quad\left(\because R_1=R\right) \\
&
\end{aligned}$
In parallel combination of such four resistances.
or
$\frac{1}{R^{\prime}}=\frac{1}{R_2}+\frac{1}{R_2}+\frac{1}{R_2}+\frac{1}{R_2}$
or $\quad \frac{1}{R^{\prime}}=\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}$
or $\frac{1}{R^{\prime}}=\frac{4}{R}+\frac{4}{R}+\frac{4}{R}+\frac{4}{R}$
or $\frac{1}{R^{\prime}}=\frac{16}{R}$
or $\quad R^{\prime}=\frac{R}{16}$
& R=\frac{\rho l}{A} \text { or } R \propto l \\
& \therefore \quad \frac{R_1}{R_2}=\frac{l_1}{l_2}=\frac{L}{L / 4}=4 \\
& \text { or } \quad R_2=\frac{R}{4} \quad\left(\because R_1=R\right) \\
&
\end{aligned}$
In parallel combination of such four resistances.
or
$\frac{1}{R^{\prime}}=\frac{1}{R_2}+\frac{1}{R_2}+\frac{1}{R_2}+\frac{1}{R_2}$
or $\quad \frac{1}{R^{\prime}}=\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}+\frac{1}{R / 4}$
or $\frac{1}{R^{\prime}}=\frac{4}{R}+\frac{4}{R}+\frac{4}{R}+\frac{4}{R}$
or $\frac{1}{R^{\prime}}=\frac{16}{R}$
or $\quad R^{\prime}=\frac{R}{16}$
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.