Series and Parallel Combination of Two Resistors

Objective:

To determine the equivalent resistance of two given resistors when connected in series and parallel using a circuit setup and verify the theoretical formula.

Apparatus Required:

A battery or power supply

A resistor (unknown resistance, say 2 Ω, 3 Ω, 5 Ω, 10 Ω etc.,)

An ammeter (to measure current)

A voltmeter (to measure potential difference)

A rheostat (variable resistor to change current)

One way plug key (Switch)

Connecting wires

Theory:

Resistors in series:

When resistors are connected in series, the same current flows through each resistor, but the voltage divides across them

Equivalent resistance (R_S)

R_S =R₁+R₂

Resistors in parallel:

Equivalent resistance (R_P)

R_P = R1R2/R1+R2

Ohm’s law Verification:

The equivalent resistance can also be determined experimentally using Ohm’s law

Req =V/I

Where, V= Voltage across combination, I= Current through the circuit

Circuit Diagram and Experimental setup

Least count of ammeter:

Least count of Voltmeter:

Procedure: [For Series Combination of Resistors]

• Connect the ammeter in series with the circuit wire and the voltmeter in parallel with the wire.
• Note the zero error of the metres.
• Calculate the least count of the metres.
• Switch on the circuit.
• Set the rheostat to a particular position and record the readings of the ammeter and voltmeter.
• Repeat steps 5 and 6 for different settings of the rheostat.
• Tabulate the readings for two individual resistors R₁ and R₂ separately
• Experiment is repeated for the combination of two resistors(series).

Series Combination of Resistors (Observations)

To Find R1:

To Find R2:

Net Effective Resistance-Series Combination of Resistors

Parallel Combination of Resistors-Procedure

• Connect the ammeter in series with the circuit wire and the voltmeter in parallel with the wire.
• Note the zero error of the metres.
• Calculate the least count of the metres.
• Switch on the circuit.
• Set the rheostat to a particular position and record the readings of the ammeter and voltmeter.
• Repeat steps 5 and 6 for different settings of the rheostat.
• Tabulate the readings for individual resistors R₁ and R₂
• Repeat the experiment for the combination of resistors (Parallel)

Parallel Combination of Two Resistors-Observations

Result: For Series Combination of Resistors

The resistance of the given resistor is found to be 3.06 Ω (From experiment)

The resistance of the given resistor is found to be 2.06 Ω (From Graphical method)

Net effective resistance is found to be 5.12 Ω (From experimental method)

Net effective resistance is found to be 5 Ω (From Theoretical method method)

For Parallel Combination of Resistors

The resistance of the given resistor is found to be 3.06 Ω (From experiment)

The resistance of the given resistor is found to be 2.06 Ω (From Experimental method)

Net effective resistance is found to be 1.2 Ω (From Experimental method)

Net effective resistance is found to be 1.23 Ω (From Theoretical method method)

Precautions:

Ensure tight connections to avoid extra resistance

Take multiple readings for accuracy.

Ammeter should always be connected in series and the voltmeter in parallel

Avoid high currents to prevent heating of resistors

Link related to the above topic

Experiment: To Determine the Focal Length of a Convex lens by Plotting Graphs Between u and v and 1/u and 1/v