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Ohm’s Law, Power, and Series-Parallel Circuits

Manual: General · Subject: Electronics

Solve DC circuit problems using resistance networks, voltage division, current division, and power relationships.

The Mathematics of DC Circuits

Ohm’s law and power

The basic relationship between voltage, current, and resistance is V=IRV = IR. Electrical power is P=VIP = VI, which can also be written as P=I2RP = I^2R or P=V2RP = \frac{V^2}{R}. These formulas are the backbone of circuit analysis and component sizing.

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Problem-solving habit

Before calculating, write down what is known, what is unknown, and the units. Most circuit mistakes come from unit confusion rather than math.

Series vs parallel

PropertySeriesParallel
CurrentSame through all componentsSplits among branches
VoltageDivides across componentsSame across each branch
Equivalent resistanceRT=R1+R2+…R_T = R_1 + R_2 + \dots1RT=1R1+1R2+…\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\dots
Failure of one partMay open the whole pathOther branches may still work

Two resistors of 2 Ω2\,\Omega and 3 Ω3\,\Omega are in series. What is the equivalent resistance?

If I=2 AI = 2\,\text{A} and R=4 ΩR = 4\,\Omega, what is the voltage?

A 12 V12\,\text{V} supply is across a 6 Ω6\,\Omega resistor. What power is dissipated?

What is the total resistance of two equal resistors of 10 Ω10\,\Omega in parallel?

Approach to network problems

  1. 1

    Step 1: Simplify obvious series or parallel groups.

  2. 2

    Step 2: Compute equivalent resistance one section at a time.

  3. 3

    Step 3: Find total current from I=V/RTI = V/R_T.

  4. 4

    Step 4: Back-substitute to find branch voltages and currents.