Question

Four copper wires of equal length are connected in series. Thecross sectional areas are 1 cm2, 2 cm2, 3cm2, and 5 cm2. A voltage of 120 V is appliedto the arrangement. What is the voltage across the 2 cm2wire in units of volt?
A)15.5
B)11.8
C)19.7
D)59
E)29.5

Answer 1

Answer:

Voltage across 2 cm² wire = 29.5 V

Explanation:

We equation for resistance,

              $R=\frac{\rho L}{A}$

Where ρ is resistivity, L is length and A is area.

Here for the four wires ρ and L is same, only area is different.

So we have

          $R_1:R_2:R_3:R_4=\frac{\rho L}{A_1}:\frac{\rho L}{A_2}:\frac{\rho L}{A_3}:\frac{\rho L}{A_3}\\\\R_1:R_2:R_3:R_4=\frac{1}{1}:\frac{1}{2}:\frac{1}{3}:\frac{1}{5}$

Here total voltage is given as 120 V,

In series connection voltage divides in the ratio of resistances

That is

              $V_1:V_2:V_3:V_4=\frac{1}{1}:\frac{1}{2}:\frac{1}{3}:\frac{1}{5}$

              $\frac{1}{1}\times x+\frac{1}{2}\times x+\frac{1}{3}\times x+\frac{1}{5}\times x=120Vx=59.02V$

Voltage across 2 cm² wire $=\frac{59.02}{2}=29.5V$

Voltage across 2 cm² wire = 29.5 V