Question

30) a Two conducting wires of same material, and of equal lengths and diameters are first connected in series and then parallel in a circuit. The ratio of heat produced in series and parallel combinations would be: 1) 1:2 2) 2:1 3) 1:4 4) 4:1​

Answer 1

The correct answer is 1 : 4. Explanation: Given, Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference.

Answer 2

Answer:

Option 3) 1 : 4

Explanation:

Given :

Two conducting wires of same material, and of equal lengths and diameters are first connected in series and then parallel in a circuit.

To find :

the ratio of heat produced in series and parallel combinations.

Solution :

We know that the resistance of a wire is given by,

⇒ $\sf R=\dfrac{\rho l}{A}$

where

ρ is the resistivity

l is the length

A is the area of cross section of the wire

Since it's given that the two conducting wires of same material, and of equal lengths and diameters, the two wires have the same resistance.

Let the resistance of each wire be R and the potential difference be V.

• The heat produced in a current carrying wire is given by, P = V²/R

When connected in series,

Equivalent resistance, R' = R + R = 2R

Heat produced, P' = V²/2R

When connected in parallel,

Equivalent resistance = R''

$\sf \dfrac{1}{R''}=\dfrac{1}{R}+\dfrac{1}{R} \\\\ \sf \dfrac{1}{R''}=\dfrac{2}{R} \\\\ \sf R'' = \dfrac{R}{2}$

Heat produced = P''

$\sf P'' = \dfrac{V^2}{\dfrac{R}{2}} \\\\ \sf P'' = \dfrac{2V^2}{R}$

The required ratio :

⇒ Heat produced in series combination : heat produced in parallel combination

⇒ P' : P''

⇒ V²/2R : 2V²/R

⇒ 1/2 : 2

⇒ 1 : 4