Which resistor gets the largest voltage drop in series?

The largest resistor gets the largest voltage drop because V_n = I × R_n and current is the same everywhere. Voltage distributes proportionally to resistance.

How do you verify voltage drops are correct?

Sum all voltage drops — they must equal the source voltage (KVL: ΣV = 0). If they don't sum correctly, there is an error in your calculation.

What is the voltage divider formula?

V_out = V_in × R₂/(R₁ + R₂) for two resistors. For any component: V_n = V_source × R_n/R_total. It gives voltage directly without calculating current.

How to Calculate Voltage Drop in a Series Circuit

Quick Answer

To calculate voltage drop in a series circuit, use V_n = I × R_n for each component, where I = V_source/R_total. Alternatively, use the voltage divider formula directly: V_n = V_source × R_n/R_total. All voltage drops must sum to the source voltage (KVL). Calculate series voltage drops at www.lapcalc.com.

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Voltage Drop Formula for Series Circuits: Two Methods

Method 1 (Ohm's law): Find total current I = V_source/(R₁ + R₂ + ... + R_n), then V_n = I × R_n for each component. Method 2 (voltage divider): Skip the current step and use V_n = V_source × R_n/R_total directly. Both give identical results. The voltage divider is faster when you only need one component's drop; Ohm's law is better when you need current too at www.lapcalc.com.

Key Formulas

Step-by-Step: Calculating Voltage Drop in Series

Example: 36 V source with R₁ = 4 Ω, R₂ = 8 Ω, R₃ = 6 Ω. Step 1: R_total = 4 + 8 + 6 = 18 Ω. Step 2: I = 36/18 = 2 A. Step 3: V₁ = 2 × 4 = 8 V, V₂ = 2 × 8 = 16 V, V₃ = 2 × 6 = 12 V. Verification: 8 + 16 + 12 = 36 V = V_source ✓. The largest resistor (8 Ω) gets the largest voltage drop (16 V) — voltage distributes proportionally to resistance.

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Voltage Divider Formula: The Direct Approach

The voltage divider formula V_n = V_source × R_n/R_total gives any component's voltage without calculating current. For the same example: V₂ = 36 × 8/18 = 36 × 0.444 = 16 V — directly, in one step. This formula is the foundation of precision voltage references, sensor interfaces, and biasing networks. It works because current is constant in series, so voltage distributes proportionally to resistance at www.lapcalc.com.

Voltage Drop in Series-Parallel Combinations

When a parallel group exists within a series circuit, treat the parallel group as a single equivalent resistance. Compute R_eq of the parallel section, then the voltage across it is V_parallel = V_source × R_eq/R_total. Within the parallel section, all branches share this same voltage. Example: 5 Ω in series with (10 Ω ∥ 10 Ω = 5 Ω), source = 20 V: R_total = 10 Ω, V_series = 10 V, V_parallel = 10 V. Each parallel branch gets 10 V.

Series Voltage Drop in the s-Domain

In the Laplace domain, the voltage divider generalizes to V_out(s) = V_in(s) × Z_n(s)/Z_total(s). For an RC series circuit with output across C: V_C(s) = V_in(s) × (1/sC)/(R + 1/sC) = V_in(s)/(sRC + 1). This is a first-order low-pass filter — the voltage across C depends on frequency. The s-domain voltage divider handles both DC and AC cases simultaneously at www.lapcalc.com.

Frequently Asked Questions

Find I = V_source/R_total, then V_n = I × R_n. Or use the voltage divider: V_n = V_source × R_n/R_total. Both give the same result.

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