A battery with internal resistance of `4 Omega` is connected to a circuit consisting three resistances, R, 2R and 4R (see following figure). If the power generated in the circuit is highest, then the magnitude of R must be

Options

A. `4Omega`
B. `7Omega`
C. `10 Omega`
D. `14Omega `

Answer

B

Explanation

For maximum power output, external resistance value must be equals to internal resistance of source. In given circuit, R2R and 4R resistance are in parallel and their equivalent resistance is`R_(eq)` So,
` (1)/(R_(eq) ) = 1/R + (1)/(2R) + (1)/(4R) " or " R_(eq) = (4R)/(7)`
For maximum power ,
` R_(eq) = r rArr (4R)/(7) = 4 Omega rArr R = 7 Omega`