For the following circuit calculate the current through each

For the following circuit, calculate the current through each resistor and the power being delivered to the each resistor. R1 is 500 Ohms, R2 is 300 Ohms, R3 is 1000 Ohms, and R4 250 Ohms.

Solution

R3 and R4 are in parallel connection, their equivalent is R\' then

1/R\' = 1/R3 + 1/R4 = 1/1000 + 1/250

R\' = 200 ohm

now R1, R2 and R\' are in series connection,

Req = R1 + R2 + R\' = 1000 Ohm

current throught battery, I = V / Req = 24/1000 = 24 x 10^-3 A or 24 mA

R1, R2 and R\' are in series with battery. hence current throught them will be same.

I1 = I2 = 24 mA

current will divide into r3 and R4.

I3 = 24 x (250) / (1000 + 250) = 4.8 mA

I4 = 24 x 1000 / (1000 + 250) = 19.2 mA

Power = I^2 R

P1 = (24 x 10^-3)^2 (500) = 0.288 W

P2 = 0.173 W

P3 = (4.8 x 10^-3) (1000) = 0.023 W

P4 = 0.092 W