Question #254467

THREE RESISTORS RA,RB AND RC ARE CONNECTED IN SERIES AND TO A 120 VOLTS

SOURCE. IF RB = 2 RA, RC = 3RA AND THE TOTAL POWER IS 200 W,

CALCULATE a.) THE RESISTANCE OF EACH RESISTOR


b.) THE POWER IN EACH RESISTOR


1
Expert's answer
2021-10-22T03:06:19-0400

The total power:


P=V2R=V2RA+RB+RC=V2RA+2RA+3RA, RA=V26P=12Ω, RB=2RA=24Ω, RC=3RA=36Ω.P=\frac {V^2}{R}=\frac{V^2}{R_{A}+R_B+R_C}=\frac{V^2}{R_{A}+2R_A+3R_A},\\\space\\ R_A=\frac{V^2}{6P}=12\Omega,\\\space\\ R_B=2R_A=24\Omega,\\\space\\ R_C=3R_A=36\Omega.

The current in the circuit is


I=PV=1.67A.I=\frac PV=1.67\text A.

The power in each resistor:


PA=I2RA=33W,PB=I2RB=67W,PC=I2RC=100W.P_A=I^2R_A=33\text W,\\ P_B=I^2R_B=67\text W,\\ P_C=I^2R_C=100\text W.


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