Question

Two conducting wires of same material and of equal lengths and of equal diameter are first connect ed on series and then in parallel in a circuit across same potential difference . Find ratio of heat produced in series and parallel combinations​

Answer 1

Answer:

Two conducting wires of same material and of equal lengths and of equal diameter are first connected on series and then in parallel in a circuit across same potential difference . Find ratio of heat produced in series and parallel combinations​

Answer - 1:4

Explanation:

Since the two wires have same material, length and diameter, they have the same resistance.

Let the resistance of each wire be R.

Let applied potential difference be V.

$R_{series} =$ R₁ + R₂ = R + R = 2R

$R_{parallel} =$ $\frac{1}{R_{1} } +\frac{1}{R_{2} } =\frac{1}{R} +\frac{1}{R} = \frac{R}{2}$

If two wires are connected in series, then its equivalent resistance is 2R Ω .

 If two wires are connected in parallel, then its equivalent resistance is R/2Ω .

Let Current drawn by series combination = V/2R  = i Amps.

Current drawn by parallel combination = V / (R/2)  = 4i Amps

 

Heat produced in series combination = i2 2R = (4iR) Watts   ......................(1)

 

Heat produced in parallel combination = 16i2 (R/2)  = ( 16iR) Watts   ......................(2)

From eqn.(1) and (2),

we get ratio of heat produced in series combination to heat produced in parallel combination = 4iR/16iR = 1/4 = 1:4

Hence ratio of heat produced in series and parallel combinations = 1:4