Two conducting wires of the same material and of equal length and equal diameters are first connected in series and then in parallel and then in circuit. What would be the ratio of heat
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Hey mate....
Since R = р × length/Cross section area
Here it is given that material [ on which resitivity depends ], length and cross section area are same. Hence, resistance of two wires is also same.
R₁ = R₂ [ Due to above reasons ]
When they are arranged in a series then,
Total R = R₁ + R₂
Total R = R₁ + R₁ = 2R₁
H = VIt
Since I = V/R
Therefore, H =
So heat produced =
When they are arranged parallel then,
Total 1/R = 1/R₁ + 1/R₂
Total 1/R = 2/R₁
Total R = R₁/2
Heat' produced =
=
Therefore,
H/H' = ( v²t / 2R₁ )/( 2v²t / R₁ )
Ratio = v²t / 2R₁ × R₁ / 2v²t = 1 / 4
Ratio = 1 : 4
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