Series Resistor Voltage Division: The Same Current Does Not Mean Equal Voltage

In one ideal series path, the same current passes through each resistor. The drop across resistor Ri is Vi = Vtotal Ri/(sum of resistances), so unequal resistances generally have unequal voltage drops.

One path gives one current

A series connection has no branching between the components considered. Add the resistances to find the total resistance, then apply I = Vtotal/Rtotal for the ideal source-and-resistor model. Each individual drop follows from that same current through Vi = IRi.

The ratio rule comes from substituting the total-current expression. It is not a separate physical law and does not apply unchanged if another branch loads the connection between two resistors. Identify the actual circuit before using a voltage-divider shortcut.

Worked unequal pair

Connect ideal resistors of 2 Ω and 4 Ω in series across 12 V. Their total resistance is 6 Ω, so current is 12/6 = 2 A. The drops are 2 × 2 = 4 V and 2 × 4 = 8 V.

Check that 4 + 8 = 12 V, matching the source. The larger resistance has the larger drop because the current is common. The same result comes directly from the ratios: 12(2/6) = 4 V and 12(4/6) = 8 V.

Use energy per charge as a check

Voltage drops add around this simple loop. Sharing the current does not mean each resistor receives the full source voltage. With equal resistors, the source voltage divides equally; with unequal resistors, the resistance ratios decide the division.

For three or more resistors in one series path, include every resistance in the denominator. A resistor’s fraction of the source voltage is its fraction of the total series resistance. Before calculating, convert all resistance values to the same unit.

Common mistake

Do not add currents as though the series components were separate parallel branches. Also distinguish the resistor’s drop from a node voltage measured relative to a chosen reference point. The ideal examples omit source internal resistance and wire resistance. They are paper circuit questions, not instructions for mains wiring or building a powered circuit.

Series mein current same hota hai; voltage resistance ke hisaab se bantta hai.

Three practice questions with worked answers

1. Resistors 3 Ω and 6 Ω are in series across 18 V. Find current and drops.

   Total resistance is 9 Ω and current is 2 A. Drops are 6 V and 12 V, summing to 18 V.

2. Two equal series resistors share an ideal 10 V source. Find each drop.

   Equal resistance fractions give 10/2 = 5 V across each.

3. A 1 Ω resistor is in series with 2 Ω and 3 Ω across 12 V. Find its drop.

   Total resistance is 6 Ω. Its share is 12(1/6) = 2 V.

Related study guides

• Electricity Class 10 Notes: Ohm’s Law, Series and Parallel, Heating Effect Numericals
• Ohm’s Law Numericals: Current, Voltage, Power and Energy

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References and authorship

Original examples and practice questions, prepared with AI assistance and editorial arithmetic review. Related definitions and methods: OpenStax: Resistors in Series and Parallel. No textbook or exam-board affiliation is claimed.