Suppose the resistances in the example are R 1 = 1.9 ?, R 2 = 3.8 ? and R 3 = 5.

Question

Suppose the resistances in the example are R1 = 1.9 ?, R2 = 3.8 ? and R3 = 5.7 ?, respectively, and a new voltage source is provided. If the current measured in the 5.7-? resistor is 5.0 A, find the following.

EXAMPLE 18.2 Three Resistors in Parallel GOAL Analyze a circuit that contains resistors connected in parallel 7 ! PROBLEM Three resistors are connected in parallel as in the figure. A potential difference of 18 V is maintained between points a and b. (a) Find the current in each resistor. (b) Calculate the power delivered to each resistor and the total power. (c) Find the equivalent resistance of the circuit. (d) Find the total power delivered to the equivalent resistance. 3.0 6.0 | 9.0 Three resistors connected in parallel. The voltage STRATEGY To get the current in each resistor we can use across each resistor is 18 v Ohm's law and the fact that the voltage drops across parallel resistors are all the same. The rest of the problem just requires substitution into the equation for power delivered to a resistor, P R, and the reciprocal-sum law for parallel resistors.

Explanation / Answer

part a)

I in R3 = 5A

V = I*R = 5 * 5.7 = 28.5 V

since all are in parallel combination so V remains same for all resistor

I1 = V/R1 = 28.5 / 1.9 = 15 A

I2 = 28.5 / 3.8 = 7.5 A

part b )

P1 = I1^2*R1 = 15^2 * 1.9 = 427.5 W

P2 = I2^2*R2 = 213.75 W

P3 = I3^2 * R3 = 142.5 W

Ptotal = P1 + P2 + P3 = 783.75 W

part c )

all are in parallel

1/Req = 1/R1 + 1/R2 + 1/R3

Req = 1.036 ohm

part d )

I = V/Req = 28.5/1.036 = 27.5 A

Peq = I^2*Req

Peq = 783.75 W

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