Answer to Question #256786 in Electrical Engineering for Joy

Question #256786
Three resistors A, B and C are connected in parallel and take a total of 7.9 amp. Resistor A takes 2.5 amp and has a resistance of 48 ohms; also, the current through B is twice as much as that through C. Calculate (a) la and Ic, (b) the line voltage and (c) Rs and Rc.
1
Expert's answer
2021-10-26T07:00:07-0400

Ia is 2.5 A as follows from the condition. The voltage drop across each resistor is equal:


"V=I_AR_A=I_BR_B=I_CR_C=120\\text{ V}."

According to Kirchhoff's current law:


"I_A+I_B+I_C=I,\\\\\nI_A+2I_C+I_C=I,\\\\\\space\\\\\nI_C=\\frac{I-I_A}{3}=1.8\\text{ A},\\\\\\space\\\\\nI_B=2I_C=3.6\\text{ A}.\\\\\nR_B=V\/I_B=33.33\\Omega,\\\\\nR_C=V\/I_C=66.67\\Omega,\\\\\\space\\\\\n\\frac1{R_\\text{equiv}}=\\frac1{R_A}+\\frac1{R_B}+\\frac1{R_C},\\\\\\space\\\\\nR_\\text{equiv}=15.19\\Omega."


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