Topic 11.512 min read
Resistors in Series
Series resistors form a single current path.
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Resistors are in series when they are connected end to end in a single path. The same current passes through every resistor.
- Req
- equivalent series resistance (Ω)
The source voltage is shared among the resistors. A larger resistance receives a larger voltage drop.
Recommended for Class 11
A series combination has one continuous current path with no junction between the connected resistors. Charge cannot choose another route, so the current is identical through every resistor.
Current in a series circuit
Current is not used up by a resistor. Charge flows continuously, while the electrical energy carried per unit charge changes across circuit elements.
Potential difference in series
The source potential difference equals the sum of the voltage drops across the individual resistors.
Applying Ohm's law to each resistor gives V1=IR1, V2=IR2 and so on.
Derivation of equivalent resistance
Because every resistance is positive, equivalent series resistance is greater than any individual resistance in the combination.
Identical resistors in series
For N identical resistors, each of resistance R:
Voltage division
The same current flows through two series resistors, so their voltage drops are proportional to their resistances.
Effect of adding a series resistor
Adding a resistor in series increases total resistance. For a fixed source voltage, the circuit current decreases according to I=V/Req.
| Series quantity | Rule |
|---|---|
| Current | Same through all resistors |
| Voltage | Individual drops add to source voltage |
| Resistance | Individual resistances add |
| Equivalent resistance | Greater than the largest individual resistance |
Worked example
Resistors of 2 Ω, 3 Ω and 5 Ω are connected in series across 20 V. Find equivalent resistance, current and each voltage drop.
The final sum checks the source voltage, so the result is internally consistent.
Practical consequence of an open circuit
If any component in a simple series path becomes disconnected, the path is broken and current stops everywhere in that branch.
Exam-ready method
- Confirm there is only one current path.
- Add resistances directly to find Req.
- Use I=V/Req for total current.
- Use the same current in every resistor.
- Calculate each voltage drop using Vi=IRi.
- Check that all voltage drops add to the source voltage.
Exam Focus
Exam Focus
Important points
- Single current path
- Same current
- Voltage-drop sum
- Req=ΣRi
- Identical resistors
- Voltage-divider relation
Important formulas
- Req=∑iRi
- I=VReq
- Vi=IRi
- V1V2=R1R2
Common exam traps
- Do not use reciprocal addition.
- Check graph/circuit topology rather than component placement alone.
Long question structure
Define series → current rule → voltage rule → Ohm's-law derivation → voltage division → example
Common Mistakes
Common Mistakes
- Mistake
Dividing current among series resistors.
- Mistake
Using the reciprocal rule for a series combination.
- Mistake
Assuming equal voltage drops for unequal resistances.
- Mistake
Forgetting that series equivalent resistance exceeds every individual resistance.
- Mistake
Failing to check that voltage drops sum to the source voltage.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
The same current flows through every series resistor.
The source voltage equals the sum of individual voltage drops.
Equivalent resistance is Req=R1+R2+⋯.
For N identical resistors, Req=NR.
Series resistors form a single current path.
Req=∑ Ri, I1=I2=⋯, V=∑ Vi
- Definition
- Series resistors form a single current path.
- Formula
- Req=∑ Ri,\quad I1=I2=⋯, V=∑ Vi
- Example
- For 2 Ω, 3 Ω and 5 Ω across 20 V, Req=10 Ω and I=2 A.
- Critical warning
- Series circuits have the same current, not the same voltage across unequal resistors.
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Exam Practice
Definition
Q1. What is a series combination of resistors?
Derivation
Q2. Derive equivalent resistance for resistors in series.
Concept
Q3. Explain voltage division in a series circuit.
Numerical
Q4. Find Req and current for 2 Ω, 3 Ω and 5 Ω in series across 20 V.
Reasoning
Q5. Why does adding a resistor in series reduce current for a fixed source voltage?