Reduce a parallel section before calculating currents and voltage drops in a mixed circuit.
Method and worked examples
Reduce a mixed circuit one section at a time. First identify components connected between the same two junctions and combine their parallel resistance using Rp1=R11+R21. Add any resistor in the unbranched series path to obtain total resistance. For an ideal source and ideal wires, total current is supply voltage divided by total resistance.
The series resistor carries total current, but the parallel resistors share only the parallel-section voltage. Calculate that voltage from ItotalRp or subtract the series drop from the supply. Then use each branch’s own resistance to find its current. Check that branch currents add to total current and the series and parallel-section voltage drops add to the supply voltage.
Example 1
An ideal 12V source supplies 2.0Ω in series with parallel resistors 6.0Ω and 3.0Ω. Find equivalent resistance, source current and branch currents.
Rp=6+36×3=2.0Ω; Rtotal =2.0+2.0=4.0Ω. Itotal =412=3.0A. Vparallel =3.0×2.0=6.0V. Branch currents are 66=1.0A and 36=2.0A, summing to 3.0A.
Example 2
In that network, the 3.0Ω branch opens while the ideal 12V source remains connected. Find the new source current and voltage across the remaining 6.0Ω resistor.
Only the 2.0Ω and 6.0Ω resistors remain in one series path. Rtotal =8.0Ω, so I=812=1.5A. The 6.0Ω resistor has V=IR=1.5×6.0=9.0V, rather than the original 6.0V.
Watch out:Only components between the same junctions share a voltage. The parallel section and a series resistor divide the source voltage.