A dc source with internal resistance `R_(0)` is loaded with three identical resistance R as shown in the figure. At what value of R will the thermal power generated in this circuit be the highest?

Options

A. `R=2R_(0)`
B. `R=3R_(0)`
C. `R=(R_(0))/(3)`
D. `R=R_(0)`

Answer

B

Explanation

The equivalent circuit may be drawn as in te figure. Resistance of the network `=R_(0)(R//3))`
Let, us assume that e.m.f of the cell is `epsilon` then current
`i=(epsilon)/(R_(0)+(R//3))`
Now, thermal power generated in the circuit
`P=i^(2)R//3=(epsilon^(2))/((R_(0)+(R//3))^(2))(R//3)`
for P to be maximum `(dP)/(dR)=0` which yields `R=3R_(0)`