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

Explanation

Equivalent emf of the circuit across, `AB` is given by
`E_(eq)(2)/(3) xx 4V`
Equivalnet resistance `rArr (1)/(r_(eq))=(1)/(3)+(1)/(6)rArrr_(eq)=2Omega`
Now, we have
Current `I=(10-4)/(2+R)=(6)/(2+R)`
`:. ` Power dissipated in R
`P=i^(2)R=(36R)/((2+R)^(2))`
for `P` to be maximum.
`(dP)/(dR)=36[((2+R)^(2)-R(2)(2+R))/((2+R)^(2))]=0`
`R=2Omega`