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
Answers
Answer:
1:4
not sure
please check the correct answer
Answer :- (c) 1:4
Step by step explanation :-
We know that,
R = ρ L/A
Since ρ , L and A is same
Then, the Resistance of these two wire will also same. --------(1)
In series combination, if two resistors are connected in series then total resistance is:-
Rs = R1 + R2
Rs = 2R -----(2) [ from - (1)]
In parallel combination the equivalent resistance is
1/Rp = 1/R1 + 1/R2
1/Rp = 1/R + 1/R [ from - (1)]
1/Rp = 2/R
Rp = R/2 ------(3)
Potential difference in both cases is same
Time taken in both cases = t
We know that,
H = I^2Rt
H = (V/R)^2Rt [ I = V/R]
H = (V^2/R)t
Heat produced in series = (V^2/Rs)t
= (V^2/2R)t (from-2)
Heat produced in parallel = (V^2/Rp)t
= (V^2/R/2)t (from-3)
= (2V^2/R)t
Hs/Hp = (V^2t/2R)/(2V^2t/R)
= (V^2t/2R) × R/(2V^2t)
= 1/4
Hs : Hp = 1:4
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