three resistance wires of equal length and equal diameter are first connected in series and then in parallel in an electric circuit if the current in the main is same in both cases what is the ratio of heat produced in them
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Let resistance be R
In first case (Series)
Rs = R + R + R
Rs = 3R
In second case
1/Rp = 1/R + 1/R + 1/R
1/Rp = 3/R
Rp = R/3
As current is same so Let it I
In first case
H = I²Rt
= I²×3R/t
= 3I²Rt (i)
In second case
H' = I²Rt
= I²×R/3×t
= I²Rt/3 (ii)
From (i) and (ii)
H/H' = 3I²Rt/I²Rt/3
H/H' = 9I²Rt/I²Rt
H = 9H'
Hope it helps you
In first case (Series)
Rs = R + R + R
Rs = 3R
In second case
1/Rp = 1/R + 1/R + 1/R
1/Rp = 3/R
Rp = R/3
As current is same so Let it I
In first case
H = I²Rt
= I²×3R/t
= 3I²Rt (i)
In second case
H' = I²Rt
= I²×R/3×t
= I²Rt/3 (ii)
From (i) and (ii)
H/H' = 3I²Rt/I²Rt/3
H/H' = 9I²Rt/I²Rt
H = 9H'
Hope it helps you
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