Determination of the equivalent resistance of two resistors are connected in parallel combination

PARALLEL COMBINATION OF RESISTORS

When two or more resistors are joined or connected if one of each resistance is connected to 1 point and the other is connected to another point is known as a parallel combination. In this combination, the voltage (potential difference) across each resistor is the same, and the current where is across the resistors. In this experiment, the current is made to flow between resistors connected in parallel combination.

Aim of the experiment :

To determine the equivalent resistance of the two resistors when connected in parallel combination.  OR to verify the law of combination of resistance in parallel combination.

Apparatus required : 

1. Meter bridge
2. Two resistors of different values
3. Galvanometer
4. Plug Key 
5. Battery
6. Jockey
7. Connecting wires

Principle of the experiment : 

01. Wheatstone's bridge is balanced when the current through the galvanometer is zero. 

02. If P, Q, R & S represent the resistances of four arms of Wheatstone's bridge. Then, P/Q = R/S

Formula : 

01. Resistance, Rp = Sl/(100 -l)

Where,

            S - Standard resistance

            l - Balancing length

02. Equivalent resistance in series, Rp = R1*R2 / R1 + R2

Where,

            R1 & R2 - Individual resistances of different values

Circuit diagram : 

The equivalent resistance of two resistors is connected in a parallel combination

Procedure : 

• The connections are made as shown in the circuit diagram respectively.

• A suitable standard resistance S is unplugged into the resistance box.

• The circuit is checked for opposite deflections by placing the Jockey at the two ends of the meter bridge wire AC alternatively.

• The Jockey is moved on the wire from end A towards C till the galvanometer shows zero deflection.

• The balancing length, l is measured. The equivalent resistance of the parallel combination is calculated using the formula. Rp = Sl/(100 -l)

• The experiment is repeated for different values of S and the average value of Rp is calculated.

Observation :

01. Resistance, R1 = ................................Ω 

02. Resistance, R2 = ................................Ω 

Tabular column :

Trial No	Resistance, S in (Ω Ohm)	Balencing length, l in (cm)	(100 - l) in (cm)	Resistance, Rp = Sl/(100 - l) in (Ω Ohm)
01.
02.
03.
04.
05.
				Mean Rp = ...........Ω

Calculations :

01. Theoretical value of equivalent resistance, Rp = R1*R2 / R1 + R2 = ................................Ω 

Result : 

The theoretical value of resistance Rp = ...............Ω is nearly equal to the experimental value of resistance Rp = ...............Ω. Hence the law of combination of resistances in series is verified.