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 β

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 = π π/π΄
Since π, 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/π _π = 1/π _1 + 1/π _2
1/π _π = 1/π + 1/π
1/π _π = 2/π
Rp = π /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 = (π/π )^2Rt
H = π^2/π ^2 Γ Rt
H = π^2/π Γ t
We know that
V = IR
I = π/π
Series
HS = π^2/π _π t
HS = π^2/((2π )) t
HS = (π^2 π‘)/2π
Parallel
Hp = π^2/π _π t
Hp = π^2/(π /2) t
HS = (2 π^2)/π t
Finding ratio
π»_π/π»_π = (((π^2 π‘)/(2 π )))/(((2π^2 π‘)/π ) )
π»_π/π»_π = (π^2 π‘)/(2 π ) Γ π /(2 π^2 π‘)
π»_π/π»_π = 1/4
β΄ HS : Hp = 1 : 4
Hence, the ratio is 1 : 4
β΄ Correct answer is (c)

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CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 12 years and a teacher from the past 16 years. He teaches Science, Accounts and English at Teachoo