NCERT Question 4 - Chapter 12 Class 10 - Electricity

Last updated at Aug. 6, 2019 by Teachoo

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. The ratio of heat produced in series and parallel combinations would be –

NCERT Question 4 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. The ratio of heat produced in series and parallel combinations would be - (a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1
Explanation: We know that,
R = ๐ ๐/๐ด
Since ๐, l and A are same,
the resistance of two wires will be same.
Let the resistance = R
Series
We know that,
In series combination
equivalent resistance is given by
RS = R1 + R2
= R + R
= 2 R
Parallel
We know that,
In parallel combination
equivalent resistance is given by
1/๐ _๐ = 1/๐ _1 + 1/๐ _2
1/๐ _๐ = 1/๐ + 1/๐
1/๐ _๐ = 2/๐
Rp = ๐ /2
The potential difference in both cases in same .
Let potential difference = V
Time taken in both cases would be same = t
We know that,
Heat generated is given by
H = I2Rt
H = (๐/๐ )^2Rt
H = ๐^2/๐ ^2 ร Rt
H = ๐^2/๐ ร t
We know that
V = IR
I = ๐/๐
Series
HS = ๐^2/๐ _๐ t
HS = ๐^2/((2๐ )) t
HS = (๐^2 ๐ก)/2๐
Parallel
Hp = ๐^2/๐ _๐ t
Hp = ๐^2/(๐ /2) t
HS = (2 ๐^2)/๐ t
Finding ratio
๐ป_๐/๐ป_๐ = (((๐^2 ๐ก)/(2 ๐ )))/(((2๐^2 ๐ก)/๐ ) )
๐ป_๐/๐ป_๐ = (๐^2 ๐ก)/(2 ๐ ) ร ๐ /(2 ๐^2 ๐ก)
๐ป_๐/๐ป_๐ = 1/4
โด HS : Hp = 1 : 4
Hence, the ratio is 1 : 4
โด Correct answer is (c)