Question

The effective resistance of a parallel connection that
consists of four wires of equal length, equal area of
cross-section and same material is 0.25 12. What
will be the effective resistance if they are connected
in series?​

Answer 1

Answer :-

Given :-

The effective resistance of a parallel connection that  consists of four wires of equal length, equal area of  cross-section and same material is 0.25 ohm.

To find :-

What  will be the effective resistance if they are connected in series?

Solution :-

Let the resistance of each wire be R.

Equivalent resistance in parallel will be :-

1/Rₑ = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄

⇒ 1/0.25 = 4/R

⇒ R = 0.25 × 4

∴ R = 1 ohm [Resistance of each wire]

Series connection :-

⇒ Rₑ = R₁ + R₂ + R₃ + R₄

⇒ Rₑ = 1 + 1 + 1 + 1

∴ Rₑ = 4 ohm is the effective resistance if connected in series.

Answer 2

Given:

Effective resistance of 4 identical wire resistance in parallel connection = 0.25 Ω

To find: Effective resistance of same wires in series connection

Calculation:

Let us assume the resistance of individual wire to be R. So, the effective resistance in parallel connection is given by:

$\frac{1}{R_{eff} } =\frac{1}{R} +\frac{1}{R} +\frac{1}{R} +\frac{1}{R} \\\frac{1}{R_{eff} }=\frac{4}{R} \\R_{eff} =\frac{R}{4} \\0.25 = \frac{R}{4} \\R=1$

So, individual resistance = 1 Ω

Now, effective resistance in series connection:

$R'_{eff} =$ R + R + R + R = 1 + 1 + 1 + 1 = 4 Ω

So, the effective resistance in case of series connection is 4Ω.

Answer:

Effective resistance in series connection is 4Ω.