Problem 19.44 Three resistors having resistances of R 1 = 1.57 , R 2 = 2.38 , an

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Problem 19.44

Three resistors having resistances of R1 = 1.57 , R2 = 2.38 , and R3 = 4.87 , are connected in parallel to a 28.2 V battery that has negligible internal resistance.

Part A

Find the equivalent resistance of the combination.

Express your answer in ohms to three significant figures.

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Part B

Find the current in each resistor.

Answer in the order indicated. Separate your answers using commas. Express your answers in amperes to three significant figures.

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Part C

Find the total current through the battery.

Express your answer in amperes to three significant figures.

Part D

Find the voltage across each resistor.

Answer in the order indicated. Separate your answers using commas. Express your answers in volts to three significant figures.

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Part E

Find the power dissipated in each resistor.

Answer in the order indicated. Separate your answers using commas. Express your answers in watts to three significant figures.

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Part F

Which resistor dissipates the most power, the one with the greatest resistance or the one with the least resistance? Explain why this should be.

Problem 19.44

Three resistors having resistances of R1 = 1.57 , R2 = 2.38 , and R3 = 4.87 , are connected in parallel to a 28.2 V battery that has negligible internal resistance.

Part A

Find the equivalent resistance of the combination.

Express your answer in ohms to three significant figures.

Req =     

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Part B

Find the current in each resistor.

Answer in the order indicated. Separate your answers using commas. Express your answers in amperes to three significant figures.

IR1,IR2,IR3 =   A  

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Part C

Find the total current through the battery.

Express your answer in amperes to three significant figures.

Part D

Find the voltage across each resistor.

Answer in the order indicated. Separate your answers using commas. Express your answers in volts to three significant figures.

VR1,VR2,VR3 =   V  

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Part E

Find the power dissipated in each resistor.

Answer in the order indicated. Separate your answers using commas. Express your answers in watts to three significant figures.

PR1,PR2,PR3 =   W  

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Part F

Which resistor dissipates the most power, the one with the greatest resistance or the one with the least resistance? Explain why this should be.

Explanation / Answer

a) 1/R = 1/R1+1/R2+1/R3

R = 0.792 ohm

b) v = iR

i = 28.2/0.792 = 35.6 amp

in parallel voltage same across all the resistors v1 = v2 = v3 = 28.2 V

i1 = 28.2/1.57 = 17.96 amp

i2 = 28.2/2.38 = 11.85 amp

i3 = 28.2/4.87 = 5.79 amp

p1 = v1*i1 = 44.27 W

p2 = v2*i1 = 67.12 W

p3 = v3*i3 = 137.3 W

R3 resistor dissipates more power across it.

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