Determination of equivalent resistance of two resistors when connected in parallel
Aim
To determine the equivalent resistance of two resistors when connected in parallel.
Materials Required
- Two resistors
- A battery eliminator
- Ammeter
- Plug key
- Connecting wires
- A piece of sandpaper
- Voltmeter
- Rheostat
Theory
When two or more resistors are connected together between two points then they are said to be connected in parallel.
In parallel combination,
- The potential difference is same across each resistor.
- The current flowing through each resistor is different.
The formula to calculate equivalent resistance in series is: 1/Rp = 1/R1 + 1/R2 + 1/R3
Circuit Diagrams



Procedure
- Setup the devices as shown in the circuit diagram (i).
- Plug the key and adjust the rheostat by sliding its variable terminal till the ammeter and the voltmeter show a reading.
- Note the readings of voltmeter and ammeter. Take out the plug or switch off the battery eliminator for a moment.
- Repeat the steps 2 and 3 for the different values of current by varying the sliding terminal of rheostat.
- Calculate resistance R1 using formula R = V/I.
- Similarly, calculate R2 and Rp (equivalent resistance in parallel) by following above steps.
Observation
For R1 :
S. No. | Voltmeter Reading (V) | Ammeter Reading (I) | Resistance (R = V/I) |
1. | 0.02 V | 0.01 A | 2 Ω |
2. | 0.04 V | 0.02 A | 2 Ω |
3. | 0.08 V | 0.04 A | 2 Ω |
Mean value of R1 = (2+2+2)/3 = 2 Ω
For R2
S. No. | Voltmeter Reading (V) | Ammeter Reading (I) | Resistance (R = V/I) |
1. | 0.01 V | 0.01 A | 1 Ω |
2. | 0.02 V | 0.02 A | 1 Ω |
3. | 0.04 V | 0.04 A | 1 Ω |
Mean value of R2 = (1+1+1)/3 = 1 Ω
For Rp
S. No. | Voltmeter Reading (V) | Ammeter Reading (I) | Resistance (R = V/I) |
1. | 0.02 V | 0.03 A | ⅔ Ω |
2. | 0.04 V | 0.06 A | ⅔ Ω |
3. | 0.06 V | 0.09 A | ⅔ Ω |
Mean value of Rp = (⅔+⅔+⅔)/3 = ⅔ Ω = 0.67 Ω
Calculation
=
+
=
+
=
Or, Rp = Ω
Result
- The calculated value of equivalent resistance, Rp = ⅔ Ω = 0.67 Ω
- The experimental value of equivalent resistance, Rp = ⅔ Ω = 0.67 Ω
- The equivalent resistance Rp is less than the individual resistances.
Precautions
- Thick copper wires should be used as connecting wires and using sandpaper, their insulation should be removed.
- The connections should be tight.
- Voltmeter should be connected in parallel with the resistor.
- To avoid unnecessary heating in the circuit, the current should be passed for a short time.
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