Which statement is true for resistors connected in series?

The total resistance is the sum of individual resistances.. Tests fundamental properties of series circuits, specifically total resistance.

If three resistors, R1, R2, and R3, are connected in series, and a current 'I' flows through R1, what is the current flowing through R3?

I. Checks understanding that current is constant in a series circuit.

A 6V battery is connected to two resistors in series: 2Ω and 4Ω. What is the potential difference across the 2Ω resistor?

2V. Requires calculating total resistance, total current, and then individual potential difference using Ohm's Law.

Physics · Class 9-10 · GCSE

Resistors in Series

Q: Three resistors of 5Ω, 10Ω, and 15Ω are connected in series across a 30V battery. What is the potential difference across the 10Ω resistor?

10V First, calculate the total resistance: R_total = 5Ω + 10Ω + 15Ω = 30Ω. Next, calculate the total current using Ohm's Law: I = V_total / R_total = 30V / 30Ω = 1A. Since it's a series circuit, the current through the 10Ω resistor is also 1A. Finally, calculate the potential difference across the 10Ω resistor: V = I * R = 1A * 10Ω = 10V.

When resistors are connected in aseriesarrangement, they are joined end-to-end, forming a single path for the current. This lesson will explain how to connect resistors in series and how the total potential difference across them relates to individual potential differences.

1What is a Series Connection?

In a series connection, components are connected one after another, so thesame currentflows through each component. Imagine a single lane road where cars must pass through each checkpoint in order.

Resistors in Series

This diagram shows three resistors connected in series to a battery. The ammeter measures the total current, and voltmeters measure potential differences.

The picture didn’t pass the label check, so here are its parts.

1R1, R2, R3 — Individual resistors
2V_total — Total potential difference
3V1, V2, V3 — Potential difference across each resistor
4A — Ammeter measuring current (I)
5Battery — Voltage source

2Connecting Resistors in Series

To connect resistors in series, simply join the end of one resistor to the beginning of the next. This creates a continuous path for the electric current to flow through all of them sequentially.

Procedure to Connect Resistors in Series

1
Identify Resistors
Take three resistors, R1, R2, and R3.
2
Connect R1 & R2
Connect one terminal of R1 to one terminal of R2.
3
Connect R2 & R3
Connect the other terminal of R2 to one terminal of R3.
4
Connect to Circuit
Connect the free terminal of R1 and the free terminal of R3 to a power source (e.g., battery).
5
Add Ammeter
Place an ammeter anywhere in the series circuit to measure current.

Common mistake: A common mistake is connecting an ammeter in parallel. Ammeters must always be connected in series to measure current correctly.

3Potential Difference in Series Circuits

In a series circuit, thetotal potential difference(voltage) across the combination is the sum of the potential differences across each individual resistor. This is a direct consequence of the conservation of energy.

Total Potential Difference in Series

V_{total} = V_1 + V_2 + V_3 + ...

$V_total$ = Total potential difference across the series combination (V)
$V_1, V_2, V_3$ = Potential difference across individual resistors (V)

Demonstrating V_total = V1 + V2 + V3

1
Set up Circuit
Connect three resistors (R1, R2, R3) in series with a battery.
2
$\text{Measure}\ V_total$
Connect a voltmeter in parallel across the entire series combination to measure V_total.
3
Measure V1
Connect a voltmeter in parallel across R1 to measure V1.
4
Measure V2
Connect a voltmeter in parallel across R2 to measure V2.
5
Measure V3
Connect a voltmeter in parallel across R3 to measure V3.
6
Compare Values
Observe that V_total is approximately equal to V1 + V2 + V3.

Did you know? Did you know that Christmas lights are often wired in series? If one bulb burns out, the entire string goes dark because the circuit is broken!

4Example and Ohm's Law

Ohm's Law ( $V = IR$ ) is fundamental to understanding series circuits. Since the current ( $I$ ) is the same through all resistors in series, the potential difference across each resistor is proportional to its resistance.

Real-life example · Calculating Potential Differences

Suppose three resistors, 2Ω, 3Ω, and 5Ω, are connected in series to a 10V battery. If the current flowing through the circuit is 1A, then V1 = 1A * 2Ω = 2V, V2 = 1A * 3Ω = 3V, and V3 = 1A * 5Ω = 5V. Notice that V_total = 2V + 3V + 5V = 10V, which matches the battery voltage.

Characteristics of Series Circuits

Characteristic	Description
Current	Same through all components
Voltage	Divides across components
Total Resistance	Sum of individual resistances
Circuit Path	Single path for current

Current
Description
Same through all components
Voltage
Description
Divides across components
Total Resistance
Description
Sum of individual resistances
Circuit Path
Description
Single path for current

5Exam Corner

Important for exams

In series, current isconstantthroughout the circuit.
Total potential difference is thesumof individual potential differences.
Total resistance in series is $R_{total} = R_1 + R_2 + R_3 + ...$
Ohm's Law ( $V=IR$ ) applies to individual resistors and the whole circuit.
Voltmeters are connected inparallelto measure potential difference.
Ammeters are connected inseriesto measure current.

Exam question · NEET 2019 style

Three resistors of 5Ω, 10Ω, and 15Ω are connected in series across a 30V battery. What is the potential difference across the 10Ω resistor?

A.5V
B.10V
C.15V
D.30V

Remember it: For series circuits, remember 'C-V-R': Current is Constant, Voltage is Variable (adds up), Resistance adds up.

Remember

Resistors in series are connectedend-to-end, forming a single path.
Thecurrentis the same through every resistor in a series circuit.
Thetotal potential differenceacross a series combination is the sum of individual potential differences.
Voltmeters are used to measurepotential differenceand are connected in parallel.
Ammeters measurecurrentand are connected in series.

Check yourself

Question 1
Which statement is true for resistors connected in series?
Question 2
If three resistors, R1, R2, and R3, are connected in series, and a current 'I' flows through R1, what is the current flowing through R3?
Question 3
A 6V battery is connected to two resistors in series: 2Ω and 4Ω. What is the potential difference across the 2Ω resistor?