Training Engineering Math DC Circuits — Ohm's Law and Kirchhoff's Laws
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DC Circuits — Ohm's Law and Kirchhoff's Laws

24 min Engineering Math

Direct-current circuit analysis is one of the first quantitative skills every engineer learns. Ohm’s law (V = IR) relates voltage, current, and resistance in a single component, while Kirchhoff’s voltage law (KVL) and current law (KCL) extend the analysis to complex networks of series and parallel resistors. These principles underpin everything from household wiring to microprocessor design. Mastering series and parallel resistance combinations, voltage dividers, and power dissipation calculations gives you the tools to analyze and design basic electrical systems.

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.

  1. $I = V/R = 12/60 = 0.2$ A.
  2. $P = VI = 12(0.2) = 2.4$ W.
Example 2

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

  1. $R_T = 10 + 20 + 30 = 60$ Ω.
  2. $I = 24/60 = 0.4$ A.
Example 3

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

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

Practice Problems

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

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