Ohm's Law, Decibels, and Signal Loss Math

Why These Formulas Matter

Every circuit you wire, every cable run you test, and every signal path you trace depends on three foundational relationships: Ohm's Law, the power equations, and the decibel scale. Whether you are troubleshooting a faulty resistor on a circuit board or measuring signal loss in a fiber or coaxial cable run, these tools tell you exactly what the numbers should be — and whether something has gone wrong. Mastering them now prepares you for the ETA CET, ETA FOI/FOT, and BICSI Installer exams, and for daily work on the job.

Safety Before You Calculate

Before measuring any live circuit, observe these non-negotiable rules:

• Lockout/Tagout (LOTO): De-energize and lock out any circuit before making physical changes to components or wiring. Never assume a circuit is dead — verify with a calibrated meter.
• PPE: Wear safety glasses and insulated gloves rated for the voltage level you are working near. Use probes and test leads rated for the circuit voltage.
• Meter polarity and range: Set your multimeter to a range above the expected value before connecting. An overloaded meter can arc or give false readings.
• Capacitor discharge: Even after power is removed, capacitors hold charge. Discharge them safely with the correct bleed resistor procedure before touching internal components.

Calculation errors can also be a safety hazard — an undersized wire or resistor that you calculated incorrectly can overheat and start a fire. Always double-check your arithmetic before specifying components.

Ohm's Law: V = IR

Ohm's Law states that the voltage (V) across a resistor equals the current (I) through it multiplied by its resistance (R).

| Find | Formula |

|------|---------|

| Voltage | V = I × R |

| Current | I = V / R |

| Resistance | R = V / I |

Units: volts (V), amperes (A), ohms (Ω). Keep your units consistent — milliamps must be converted to amps before you plug into the formula.

Power Equations

Electrical power (P), measured in watts (W), describes how fast a circuit converts electrical energy. Three equivalent forms exist:

• P = I × V — use when you know current and voltage
• P = V² / R — use when you know voltage and resistance
• P = I² × R — use when you know current and resistance

These are derived by substituting Ohm's Law into P = IV; all three are mathematically equivalent. Power calculations are critical for selecting fuses, wires, and power supplies that will not overheat.

The Decibel (dB) Scale

In telecom and electronics, signal levels often span many orders of magnitude. The decibel compresses that range into manageable numbers and allows you to add or subtract gains and losses instead of multiplying or dividing ratios.

For power ratios:

> dB = 10 × log₁₀(P₂ / P₁)

For voltage ratios (when comparing signals across equal impedances):

> dB = 20 × log₁₀(V₂ / V₁)

Key reference points to memorize:

| dB value | Power ratio | Meaning |

|----------|-------------|---------|

| 0 dB | 1:1 | No change |

| +3 dB | ≈ 2:1 | Power doubled |

| −3 dB | ≈ 1:2 | Power halved |

| +10 dB | 10:1 | Power ×10 |

| −10 dB | 1:10 | Power ÷10 |

A positive dB value means gain (amplifier); a negative dB value means loss (cable attenuation, splitter, connector). In a cable system, losses accumulate — you simply add the dB losses for each segment and connector in the path.

dBm: Absolute Power Reference

You will also see dBm, which expresses power relative to 1 milliwatt:

> dBm = 10 × log₁₀(P / 1 mW)

For example, 10 mW = +10 dBm; 0.1 mW = −10 dBm. Fiber optic link budgets and RF signal-level measurements are almost always expressed in dBm.

Applying dB to Cable Loss

Suppose a coaxial cable segment has a rated attenuation of 3 dB at a given frequency. If you input 20 mW, the output power is 10 mW. If you then pass through a connector rated at 0.5 dB loss, your total loss is 3.5 dB. You do not multiply; you add the losses. This additive property is the main reason the telecom industry uses decibels every day.

Using a Scientific Calculator

To evaluate log₁₀ on most scientific calculators:

1. Enter the argument (the number inside the log).

2. Press the log key (not ln, which is the natural log).

3. Multiply the result by 10 (for power) or 20 (for voltage).

Practice until this sequence is automatic — exam problems are timed.

Connecting to Your Credentials

• ETA CET: Tests Ohm's Law and power equations directly in the DC and AC sections.
• ETA FOI/FOT: Requires dB and dBm calculations for fiber link budget analysis.
• BICSI Installer: Expects understanding of signal loss in copper and fiber cabling systems, expressed in dB.