.svg)
Two conducting wires of the same material and 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
(c) 1 : 4
Explanation : The wire is made of the same conducting material, having equal length and width, thus each wire has the same resistance = R
For series combination :
RS = R + R
= 2R
For parallel combination :
1/RP = 1/R + 1/R
1/RP = 2/R
RP = R/2
Electric Power
P = V2t/R
For series combination, the heat released
PS = V2t/RS
PS = V2t/2R
For parallel combination, the heat released :
PP = V2t/RP
PP = V2t/(R/2)
⇒ PS/PP = (V2t/2R) / (V2t/(R/2))
PS/PP = (V2t/2R) X (R/2)/V2t // Cancelling V2t by V2t
PS/PP = 1/2R X R/2 // Cancelling R by R
PS/PP = 1/2 x 1/2
PS/PP = 1/4
Hence.
PS : PP = 1 : 4
.avif){kind=small}
.svg){kind=logo}
