Basic Electrical Math & Circuit Theory

Ohm's Law, Watt's Law, Series vs. Parallel resistance calculations

While the written aptitude test focuses on pure math and reading comprehension, oral interviews and subsequent pre-apprenticeship coursework evaluate your foundational electrical reasoning. Mastering Ohm's Law, Watt's Law, and basic series-parallel circuits provides an immediate edge in interview ranking.

On the Test

Fundamental formulas frequently tested in trade math sections, apprentice screening, and JATC interviews.

•Ohm's Law: Voltage (V) = Current (I) * Resistance (R).
•Watt's Law (Power): Power (P) = Voltage (V) * Current (I) = I^2 * R = V^2 / R.
•Series Circuits: Current is identical throughout; total resistance is R1 + R2 + R3; voltages drop additively.
•Parallel Circuits: Voltage is identical across all branches; currents add; total resistance is 1 / (1/R1 + 1/R2).
•Transformer Turns Ratio: Vp / Vs = Np / Ns = Is / Ip (power in equals power out).
⚠Common trap: Total resistance in parallel is ALWAYS smaller than the smallest individual resistor. If you calculate total resistance of 10 ohms and 20 ohms in parallel and get 30 ohms, you used the series formula.

The Fundamental Triangle: Ohm's Law (V = I * R)

Voltage (V, measured in Volts) is electrical potential difference or electromotive force. Current (I, measured in Amperes) is the rate of electron flow. Resistance (R, measured in Ohms, Omega) is opposition to electron flow.

Ohm's Law governs all DC circuits: V = I * R. Rearranging yields: I = V / R and R = V / I.

Example: A 120V circuit powers an electric heater with a resistance of 15 Ohms. Calculate the current: I = 120V / 15 Ohms = 8 Amperes.

Electrical Power & Watt's Law (P = V * I)

Electrical power (P, measured in Watts) is the rate at which electrical energy is converted into work, heat, or light. One Watt equals one Joule per second.

Watt's Law states: P = V * I. By substituting Ohm's Law (V = I * R), we obtain two additional essential power formulas: P = I^2 * R and P = V^2 / R.

Example: An appliance draws 10 Amperes at 240 Volts. Power consumption is: P = 240V * 10A = 2,400 Watts (or 2.4 kW). If the appliance operates for 5 hours, total energy consumed is 2.4 kW * 5h = 12 kilowatt-hours (kWh).

Series Circuit Analysis

In a series circuit, components are connected end-to-end, forming a single continuous loop for current flow. Current (I) has only one path, meaning current is constant through every component: I_total = I1 = I2 = I3.

Total resistance is the direct algebraic sum of individual resistances: R_total = R1 + R2 + R3.

Total voltage drops across each resistor according to Ohm's Law (Kirchhoff's Voltage Law): V_total = V1 + V2 + V3. If three 20-Ohm resistors are in series across a 120V source, R_total = 60 Ohms, I = 120 / 60 = 2A, and each resistor drops 2A * 20 Ohms = 40V.

Parallel Circuit Analysis

In a parallel circuit, each component is connected across the common voltage terminals. Voltage across every branch is identical: V_total = V1 = V2 = V3.

Total current divides among branches (Kirchhoff's Current Law): I_total = I1 + I2 + I3.

Total resistance in parallel is calculated using reciprocals: 1 / R_total = 1 / R1 + 1 / R2 + 1 / R3. For two resistors: R_total = (R1 * R2) / (R1 + R2). Example: A 20-Ohm and 30-Ohm resistor in parallel: R_total = (20 * 30) / (20 + 30) = 600 / 50 = 12 Ohms. Notice 12 Ohms is less than 20 Ohms.

AC Waveforms and Transformer Turns Ratios

Alternating Current (AC) reverses direction periodically in a sinusoidal waveform. In North America, the standard utility frequency is 60 Hertz (cycles per second).

Transformers transfer AC electrical energy between circuits through electromagnetic induction without changing frequency. They step voltage up or down based on turns ratio: Vp / Vs = Np / Ns, where Vp is primary voltage, Vs is secondary voltage, Np is primary turns, and Ns is secondary turns.

Example: A step-down transformer has 1,200 primary turns and 120 secondary turns. If primary voltage is 480V: Vs = 480 * (120 / 1200) = 48V. Assuming negligible losses, power in equals power out (Pin = Pout), so secondary current steps up proportionally: Is = Ip * (Np / Ns).

Key Takeaways

✓Memorize the power formulas: P = VI, P = I^2*R, and P = V^2/R. You can solve any electrical math question with these three.
✓In parallel, total resistance is always less than the lowest branch resistance.
✓Two identical resistors in parallel have a total resistance of exactly half of one resistor (e.g. two 50-Ohm resistors = 25 Ohms).
✓Step-down transformers reduce voltage but increase available current proportionally.

Key Terms

Voltage (V)

Electromotive force or potential difference in Volts.

Current (I)

Rate of charge flow measured in Amperes (Coulombs/sec).

Resistance (R)

Opposition to current flow measured in Ohms.

Power (P)

Rate of electrical energy dissipation in Watts.

Series Circuit

Circuit with a single path; current is identical in all parts.

Parallel Circuit

Circuit with multiple branches; voltage is identical across branches.

Transformer

Device transferring AC energy between circuits via electromagnetic induction.

Frequency (Hz)

Cycles per second of an alternating current waveform (60 Hz standard).

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