Question

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.

Answer 1

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:

$$I_A+I_B+I_C=I,\\ I_A+2I_C+I_C=I,\\\space\\ I_C=\frac{I-I_A}{3}=1.8\text{ A},\\\space\\ I_B=2I_C=3.6\text{ A}.\\ R_B=V/I_B=33.33\Omega,\\ R_C=V/I_C=66.67\Omega,\\\space\\ \frac1{R_\text{equiv}}=\frac1{R_A}+\frac1{R_B}+\frac1{R_C},\\\space\\ R_\text{equiv}=15.19\Omega.$$