Question
Download Solution PDFTwo conducting wires of the same material and of equal lengths and equal diameters are first connected in parallel and then in series in a circuit across the same potential difference. The ratio of heat produced in parallel and series combinations is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Let the resistance of each wire be R.
Parallel Combination:
Equivalent resistance, Rparallel = R / 2
Heat produced, Hparallel ∝ 1 / Rparallel
⇒ Hparallel ∝ 1 / (R / 2) = 2 / R
Series Combination:
Equivalent resistance, Rseries = 2R
Heat produced, Hseries ∝ 1 / Rseries
⇒ Hseries ∝ 1 / (2R)
Ratio of Heat Produced:
Ratio = Hparallel : Hseries
⇒ Ratio = (2 / R) : (1 / (2R))
⇒ Ratio = 4 : 1
∴ The ratio of heat produced in parallel and series combinations is 4:1.
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