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

Voltage across 2 cm² wire = 29.5 V

Step-by-step explanation:

We equation for resistance,

`R=(\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=(\rho L)/(A_1):(\rho L)/(A_2):(\rho L)/(A_3):(\rho L)/(A_3)\\\\R_1:R_2:R_3:R_4=(1)/(1):(1)/(2):(1)/(3):(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=(1)/(1):(1)/(2):(1)/(3):(1)/(5)`

`(1)/(1)* x+(1)/(2)* x+(1)/(3)* x+(1)/(5)* x=120Vx=59.02V`

Voltage across 2 cm² wire
`=(59.02)/(2)=29.5V`

Voltage across 2 cm² wire = 29.5 V