Verify the Laws of Combination of Resistances

Aim

To verify the laws of combination of resistances (series and parallel) using a metre bridge.

Apparatus and Material Required

• Metre bridge,
• Galvanometer,
• Two different standard resistors,
• A resistance box,
• A rheostat
• A jockey,
• One-way plug key,
• Battery eliminator,
• Thick connecting wires,
• A piece of sandpaper

Principle

When two resistances \(R_1\) and \(R_2\) are connected in series, the resistance of the combination \(R_S\) is given by \[R_S = R_1 + R_2\]

When these two resistances are connected in parallel, the resistance of the combination \(R_P\) is given by \[\frac{1}{R_P} = \frac{1}{R_1} + \frac{1}{R_2}\] \[R_P = \frac{R_1R_2}{R_1+R_2}\]

Procedure

Set up:

• Clean the ends of the connecting wires with the help of sandpaper in order to remove any insulating coating on them.
• Tighten all plugs in the resistance box \(R_{BOX}\) by rotating and pressing each of them.
• Set up the circuit as shown in the adjoining diagram.

Resistances in series

• Put the series combination of the two resistors in the gap E.
• Introduce some resistance,\(R_{BOX}\) in the circuit from the resistance box. Bring the jockey J in contact with terminal A first and then with terminal B. Note the direction in which pointer of the galvanometer gets deflected in each case. Make sure that jockey remains in contact with the wire for a fraction of a second. If the galvanometer shows deflection on both sides of its zero mark for these two points of contact of the jockey, null point will be somewhere on the wire AB.
• If it is not so, adjust resistance \(R_{BOX}\) so that the null point is somewhere in the middle of the wire AB.
• Note resistance \(R_{BOX}\) and lengths AD and DB in the observation table. Calculate the experimental value \(R_S\) of the series combination of the resistances.
• Repeat the experiment for three more values of resistances \(R_{BOX}\). Obtain the mean value of series combinations of the resistances.

Resistances in parallel

1. Put the parallel combination of the two resistors in the gap E.
2. As in the above, chose a value of resistance, \(R_{BOX}\), such that null point lies somewhere in the middle of the wire AB.
3. Note resistance \(R_{BOX}\) and lengths AD and DB in the observation table. Calculate the experimental value \(R_P\) of the parallel combination of the resistances.
4. Repeat the experiment for three more values of resistances \(R_{BOX}\). Obtain the mean value of parallel combination of the resistances.

Observations

\(R_1 = 10 \Omega\), \(R_2 = 20 \Omega\)

Below is the Experimental value of “Equivalence of the combination of resistances in Series”

Below is the Experimental value of “Equivalence of the combination of resistances in Parallel”

Calculations

Combination of Resistances in Series

Theoretical value = \(R_S = R_1 + R_2\) = 10 + 20 = 30 \(\Omega\)

Experimental Value
Avg. \(R_S\) =\(\frac{29.1+29.4+30.4+29.3}{4} = 29.6 \Omega\)

Combination of Resistances in Parallel

\(\frac{1}{R_P} = \frac{1}{R_1} + \frac{1}{R_2}\)

Theoretical value = \(R_P = \frac{R_1R_2}{R_1+R_2}\) = \(\frac{10\cdot 20}{10+20} = 3.33 \Omega\)

Avg. \(R_S\) =\(\frac{3.3+3.2+3.3+3.4}{4} = 3.3 \Omega\)

Results

Equivalent resistance of Combination of Resistances in Series is \(29.6 \Omega \).

Equivalent resistance of Combination of Resistances in Parallel is \(3.3 \Omega \).

Precautions

1. All the connections and plugs should be tight.
2. Jockey should be moved gently over the metre bridge wire.
3. Only insert the key while taking observations to avoid the heating of the wire, which can impact its resistivity.
4. Null points should be in the middle of the wire (30 cm to 70 cm).

Sources of error

1. Effect of end resistances due to copper strips, connecting screws, may affect the measurement.
2. The resistances of end pieces/metal strips may not be negligible. The error introduced by it can be reduced by interchanging the known and unknown resistances in gaps E and F.
3. Galvanometer pointer is expected to be at zero when no current flows through it. However, many times it is observed that it is not so. In such cases, pointer has to be adjusted to zero by gently moving the screw below the scale with the help of a screw driver. Otherwise null point must be obtained by tapping the jockey on the wire.

Conclusion

The experiment successfully verified the laws of combination of resistances for both series and parallel configurations using a meter bridge. The measured values for equivalent resistance were consistent with theoretical predictions based on Ohm’s law and Kirchhoff’s laws.

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Reference: NCERT Lab Manual