Question

Raj has two wires. Both wires are of same material but are of different lengths and cross - section.Raj connect the two wires in series and observe change. What is the change? Why?
(1) a) No change
b) Area increases
c) Resistance increases as length increases
d) Resistance increases as area increases​

Answer 1

Given:

Raj has two wires. Both wires are of same material but are of different lengths and cross - section.Raj connect the two wires in series and observe change.

To find:

What change was observed?

Calculation:

Let the resistance of 1st wire be R1:

$\rm \: R1 = \rho \times \dfrac{L_{1}}{a_{1}}$

Now, resistance of 2nd wire be R2:

$\rm \: R2 = \rho \times \dfrac{L_{2}}{a_{2}}$

Now, when connected in series, the net resistance will be :

$\rm R_{net} = R1 + R2$

$\rm \implies R_{net} > R1 \: and \: R_{net} > R2$

So, net resistance increases due to increased in effective length.

• It is analogous to putting a wire with net resistance of R_(net) having a higher length than individual wires.