Multiloop Circuits — Question 1

Question 1

Branch currents satisfy a junction equation and a global power balance

An ideal 24.0 V source feeds parallel 6.00 ohm and 12.0 ohm resistors. All connecting wires have zero resistance.

1. Find the two branch currents, total source current and equivalent resistance.

2. Calculate the power in each resistor and verify source power equals their sum.

Question 1 - Solution

Branch currents satisfy a junction equation and a global power balance

(a) Method and calculation

$$I_1=24/6=4.00\,\mathrm A,\quad I_2=24/12=2.00\,\mathrm A.$$$$I_s=I_1+I_2=6.00\,\mathrm A,\quad R_{\mathrm{eq}}=24/6=4.00\,\Omega.$$

(b) Interpretation and further calculation

$$P_1=I_1^2R_1=96.0\,\mathrm W,\quad P_2=I_2^2R_2=48.0\,\mathrm W.$$$$P_s=24(6)=144\,\mathrm W=P_1+P_2.$$

Physical check

Equal branch voltage does not imply equal branch current.