R1 = 100 , R2 = 300 , R3 = 200 In the circuit diagram below, the total current f

Question

R1 = 100 , R2 = 300 , R3 = 200
In the circuit diagram below, the total current flowing through the circuit is 1 Amp, calculate the total power using P = I2*Rtotal , and then verify the answer by calculating power dissipated in each of the resistors and doing the sum.

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this is what i have for total power:

R|| (1,2) = R1R2 / (R1 + R2) = 100 * 300 / (100 + 300 ) = 75

Rtotal = R3 + R|| (1,2) = 200 + 75 = 275

P = I2*Rtotal = 1A2 *275 = 275 W

I don't get the same value when adding up the powers for each individual resistor.

i calculated V = P / I = 275 W / 1 A = 275 V then used

I1 = (275 V / 100 ) = 2.75 A                        P1 = (2.75A)2 (100 ) = 176.89 W

I2 = (275 V / 300 ) = 0.917 A                      P2 = (0.917A)2 (300 ) = 58.87 W

I3 = (275 V / 200 ) = 1.375 A                      P3 = (1.375A)2 (200 ) = 88.45 W

obviously i went wrong somewhere??

Explanation / Answer

Yeah what you did in the first part is correct,but during power dissipation in individual circuits you are using total voltage in calculation of i1,as potential decreases as R3 resistor is connected in series.Instead of 275V you should use,(275-i3R3) for calculating i1.similarly for i2 also. i1=(275-1*200)/100=0.75A------->P1=i1^2R1=(0.75)^2*100=56.25W i2=(275-1*200)/300=0.25A------->P2=i2^2R1=(0.25)^2*100=6.25W for R3---->P3=i3^2R3=1^2*200=200W P=P1+P2+P3 =56.25+6.25+200 =275W which is same as you did for 1st part

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