Resistors `P , Q , and R` in the circuit have equal resistances. If the battery is supplying a total power of `12 W` , what is the power dissipated as heat in resistors `R`?

Options

A. `2 W`
B. `6 W`
C. `3 W`
D. `8 W`

Answer

A

Explanation

Let resistors `P, Q , and R` have resistance `r`. The effective resistance across the source is
`R_(eff) = r |\| r = r + (( r ) ( r ))/( r + r) = r + ( r ) /(2) = ( 3 r) /(2)`
Current drawn from source is
`I_(s)^(2) R_(eff) = 12`
or `I_(s) = sqrt((12)/(R_(eff))) = sqrt((8)/(r )) A`
Since `Q and R` have equal resistance `r`, each draws a current of `I` , which is given by
`I = (1)/(2) I, sqrt((2)/( r ))r = 2 W`