Question

two identical wires are first connected in series and then in parallel to a source of supply find the ratio of the heat produced in two cases​

Answer 1

Let the resistance of two wires be R and R

When connected in series the effective resistance is = R + R = 2R

When connected in parallel the effective resistance is = R ×R / R+R = R/2

By joule's law of heating

H (proportinal to ) R

Therefore the ratio = 2R/(R/2)

= 4:1

Answer 2

Answer:

1:4

Explanation:

Let us assume the resistance of the wires if connected in series be Rs

and resistance of the wires if connected in parallel be Rp

For series combination

Total resistance R = R1 + R2 + ……

So calculating the series resistance we get

RS =R+R=2R------------eq 1

For parallel combination

Total resistance 1/R = 1/R1 + 1/R2 + ….

So calculating the parallel resistance we get

1/ RP = 1/R +1/R

1/ RP = 2/R

RP =R/2------------eq 2

Combine equations 1 and 2 we get,

Rp/Rs = (R/2)/2R = 1/4

The ratio of heat produced is 1/4

Answer

Hence the ratio of the resistances is 1:4