In a circuit shown in figure if the internal resistances of the sources are negligible then at what value of resistance `R` will the thermal power generated in it will be the maximum. What is the value of maximum power?

Answer

A, B, D

Explanation

Applying Kirchhoff's laws in two loops we have

`10-i_1R-6+3i_2=0` …………i
`6-6(i_1+i_2)-3i_2=0`…………ii
Solving these two equations we get
`i_1=6/(R+2)`
Power developed in `R`
`P=i_1^2R=36/((R+2)^2)`............iii
For power to be maximum,
`(dP)/(dR)=0`
`:. (R+2)^2(36)-(36R)(2)(R+2)=0`
`or R+2-2R=0`
`:. R=2Omega`
From maximum power from eqn iii we have
`P_(max)=4.5W`