1 / 5

DC Circuits — Ohm's Law and Kirchhoff's Laws

24 min Engineering Math

DC Circuits

Every electronic device runs on Ohm's law and Kirchhoff's laws — simple linear equations.

Ohm's Law

$$V = IR$$

Voltage = Current × Resistance. This is $y = mx$ — a linear function.

Kirchhoff's Laws

KCL (junction): currents in = currents out.

KVL (loop): sum of voltages around a loop = 0.

Series and Parallel Resistors

Series: $R_T = R_1 + R_2 + \cdots$

Parallel: $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$

Example 1

A 12 V battery drives a 60 Ω resistor. Find current and power.

$I = V/R = 12/60 = 0.2$ A.

$P = VI = 12(0.2) = 2.4$ W.

Example 2

Three resistors (10, 20, 30 Ω) in series with a 24 V battery. Find current.

$R_T = 10 + 20 + 30 = 60$ Ω.

$I = 24/60 = 0.4$ A.

Example 3

Two resistors (100 Ω and 200 Ω) in parallel. Find $R_T$.

$\frac{1}{R_T} = \frac{1}{100} + \frac{1}{200} = \frac{3}{200}$ → $R_T = 66.7$ Ω.

1. Find current through a 150 Ω resistor with 9 V applied.

2. $R_1 = 50$ Ω and $R_2 = 50$ Ω in parallel. Find $R_T$.

3. Three resistors (20, 30, 50 Ω) in series. Find $R_T$.

4. A 5 A current flows through a 12 Ω resistor. Find voltage drop.

5. Power dissipated by a 100 Ω resistor carrying 0.3 A?

6. Using KVL: a loop has a 12 V source and two resistors dropping 5 V and $V_2$. Find $V_2$.

Show Answer Key

1. $I = 9/150 = 0.06$ A = 60 mA

2. $R_T = 25$ Ω

3. $R_T = 100$ Ω

4. $V = 5 \times 12 = 60$ V

5. $P = I^2 R = 0.09 \times 100 = 9$ W

6. $V_2 = 12 - 5 = 7$ V