Chapter 11

NCERT
Class 10
Science
Solutions
4. 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

Question:

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

Answer:

(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

Buy Latest Books

Teacher's Corner