The figure shows a circuit with a battery and five resistors. What is the curren

Question

The figure shows a circuit with a battery and five resistors. What is the current through and the potential difference across each resistor? R_1|= 10.0 ohm, R_2|= 4.00 ohm, R_3|= 11.0 ohm, R_4|= 12.0 ohm, R_5|= 13.0 ohm, and V = 37.0 V. Current through R_1|: Potential difference across R_1|: Current through R_2|: Potential difference across R_2|: Current through R_3|: Potential difference across R_3|: Current through R_4|: Potential difference across R_4|: Current through R_5|: Potential difference across R_5|:

Explanation / Answer

from figure
R34 = R3*R4/(R3+R4) = 11*12/(11+12) = 5.74 ohms

R234 = R2 + R34 = 4 + 5.74 = 9.74 ohms

R2345 = R234*R5/(R234 + R5) = 9.74*13/(9.74+13) = 5.57 A

Rnet = R1 + R2345 = 10 + 5.57 = 15.57 ohms

current through R1, I1 = V/Rnet = 37/15.57 = 2.38 A

current through R2, I2 = I1*R5/(R234 + R5) = 2.38*13/(9.74 + 13) = 1.36 A

current through R3, I3 = I2*R4/(R3 + R4) = 1.36*12/(11+12) = 0.709 A

current through R4, I4 = I2*R3/(R3 + R4) = 1.36*11/(11+12) = 0.65 A

current through R5, I5 = I1*R234/(R234 + R5) = 2.38*9.74/(9.74 + 13) = 1.02 A

V1 = I1*R1 = 2.38*10 = 23.8 volts

V2 = I2*R2 = 1.36*4 = 5.44 volts

V3 = I3*R3 = 0.709*11 = 7.8 volts

V4 = I4*R4 = 0.65*12 = 7.8 volts

V5 = I5*R5 = 1.02*13 = 13.26 volts

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