Two conducting wires of the same material and of equal lengths and equal diametersare first connected in series and then parallel in a circuit across the same potentialdifference.

Q.4:-  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 –(a) 1:2 (b) 2:1 (c) 1:4 (d) 4:1 

 

Answer:-

(c) Heat produced in the circuit is inversely proportional to the resistance R.
Let RS be the equivalent resistances of the wires if connected in series and R be the equivalent resistances of the wires if connected in parallel
Then RS =R+R=2R
And 1/ RP = 1/R +1/R
       1/ RP = 2/R
Or        RP =R/2
Now the ratio of heat produced is given by
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      = 1/4