Question 17 of 31advanced🔧 ApplyMCQ1 mark

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 –

Exercise: EXERCISES | Q: 4 | (Page Page 23)
For More Understanding

Explanation

Since both wires are of the same material, equal length and equal diameter, each wire has the same resistance, say R. In series combination, the equivalent resistance Rs = R + R = 2R. In parallel combination, the equivalent resistance Rp = R/2. The heat produced is given by H = V²t/R. For series: Hs = V²t/(2R). For parallel: Hp = V²t/(R/2) = 2V²t/R. The ratio Hs:Hp = [V²t/(2R)] : [2V²t/R] = 1:4.

Solution Steps

  1. Step 1: Let resistance of each wire = R (since same material, length and diameter)

  2. Step 2: Series combination: Rs = R + R = 2R

  3. Step 3: Parallel combination: Rp = R×R/(R+R) = R/2

  4. Step 4: Heat produced H = V²t/R (using Joule's heating formula)

  5. Step 5: Heat in series: Hs = V²t/(2R)

  6. Step 6: Heat in parallel: Hp = V²t/(R/2) = 2V²t/R

  7. Step 7: Ratio Hs:Hp = [V²t/(2R)] : [2V²t/R] = 1:4

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