Class 10

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

Fig. (i)
Fig. (ii)
Fig. (iii)

Procedure

  1. Setup the devices as shown in the circuit diagram (i).
  2. Plug the key and adjust the rheostat by sliding its variable terminal till the ammeter and the voltmeter show a reading.
  3. Note the readings of voltmeter and ammeter. Take out the plug or switch off the battery eliminator for a moment.
  4. Repeat the steps 2 and 3 for the different values of current by varying the sliding terminal of rheostat.
  5. Calculate resistance R1 using formula R = V/I.
  6. Similarly, calculate R2 and Rp (equivalent resistance in parallel) by following above steps.

Observations

For R1 :

S. No.Voltmeter Reading (V)Ammeter Reading (I)Resistance (R = V/I)
1.0.02 V0.01 A2 Ω
2.0.04 V0.02 A2 Ω
3.0.08 V0.04 A2 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 V0.01 A1 Ω
2.0.02 V0.02 A1 Ω
3.0.04 V0.04 A1 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 V0.03 A⅔ Ω
2.0.04 V0.06 A⅔ Ω
3.0.06 V0.09 A⅔ Ω

Mean value of Rp = (⅔+⅔+⅔)/3 = ⅔ Ω = 0.67 Ω

*These observations may be different for different voltmeter, ammeter and resistors.

Calculation

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} = \frac{1}{2} + \frac{1}{1} = \frac{3}{2}

Or, Rp = \frac{2}{3} 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

  1. Thick copper wires should be used as connecting wires and using sandpaper, their insulation should be removed.
  2. The connections should be tight.
  3. Voltmeter should be connected in parallel with the resistor.
  4. To avoid unnecessary heating in the circuit, the current should be passed for a short time.
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