Question

Two resistors A and B of resistance 4 Ω and 6 Ω respectively are connected in parallel. The combination is connected across a 6 volt battery of negligible resistance. Calculate: (i) the power supplied by the battery, (ii) the power dissipated in each resistor.

Answer 1

Given,
Resistance, R_A = 4Ω
Resistance, R_B = 6Ω
Voltage, V = 6V
(i) As resistance are connected in parallel

Equivalent Resistance = `1/R = 1/R_A+1/R_B`

                                      `1/R = 1/4 +1/6=1/24`

                                    R  = 2.4 Ω

As  Power ,                 p= `V^2/R`

                                    = `(6)^2/2.4` = 15 W

(ii) Power dissipation across each resistor, p = VI 

Current across resistor  `R_ A , I_A` = `V/R_A`

                                                `I_A = 6/4 =1.5A `

Power dissipation across resistor RA,

P = `VI_A` = 6  x 1.5 = 9w 

(ii) Current across resistor  `R_B , I_B = V/R_B`

                                         `I_B = 6/6=1A`

Power dissipation across resistor `R_B,`

                                                     P = `VI_B = 6 xx 1 = 6`w