Question

One end of the Nichrome wire of length $2L$ and cross-sectional area $A$ is attached to an end of another Nichrome wire of length $L$ and cross-sectional area $2A$. If the free end of the longer wire is at an electric potential of 8.0 volts, and the free end of the shorter wire is at an electric potential of 1.0 volt, the potential at the junction of the two wires is equal to

• A. $2.4V$
• B. $3.2V$
• C. $4.5V$
• D. $5.6V$

Answer 1

The correct option is A $2.4V$

Let $V_1$, $I_1$ be the voltage and current for Nichrome wire of length $2L$ and cross-sectional area $A$.

$V_2,I_2$ be the voltage and current for Nichrome wire of length $L$ and cross-sectional area $2A$.

According to Kirchhoff's law,
$I_1=\frac{(V_1-V)}{R_1}$

$I_2=\frac{(V-V_2)}{R_2}$
where R is thee resistance of Nicrome wire,
$R=\frac{\rho l}{A}$

Hence,
$R_1=\frac{\rho 2L}{A}=2R$

$R_2=\frac{\rho L}{2A}=0.5R$

Since current entering from one end leaves from other end,
$I_1=I_2$
$\frac{8-V}{2}=\frac{V-1}{0.5}$
$V=\frac{6}{2.5}=2.4V$