Three resistors having resistances of R 1 = 1.46 ? , R 2 = 2.44 ? , and R 3 = 4.

Question

Three resistors having resistances of R1 = 1.46?, R2 = 2.44? , and R3 = 4.85? respectively, are connected in parallel to a 27.6V battery that has negligible internal resistance.

A) Find the equivalent resistance of the combination.

B) Find the current in each resistor.

C) Find the total current through the battery.

D) Find the voltage across each resistor.

E) Find the power dissipated in each resistor.

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 = 1/1.46 + 1/2.44 + 1/4.85

R=1/(1/1.46 + 1/2.44 + 1/4.85)=0.769 ohms

B) things in parallel share voltage

I1 = 27.6/1.46=18.9 A

I2 = 27.6/2.44=11.31 A

I3 = 27.6/4.85=5.69 A

C) total I = 18.9 + 11.31+5.69=35.9 A

D) V1 = V2 = V3 = 27.6 V

E ) P1 = 27.6^2/1.46=521.75 W

P2 = 27.6^2/2.44=312.2 W

P3 = 27.6^2/4.85=157.1 W

F) least resistance since it gets most current

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