Lab Manual: Resistors in Series | Lab Manuals for Class 10 PDF Download

Objective

To determine the equivalent resistance of two resistors, when connected in series combination.

Materials Required
Two standard resistance coils (or resistors), ammeter (0-1.5A), voltmeter (0-1.5V), one-way key, low resistance rheostat, connecting wires, a piece of sand paper and ceil or battery eliminator.

Theory/Principle

The end-to-end connection of two or more resistors is said to be series combination, if they. provide only one path to the flow of current, i.e. same current would be flown through each resistor.
Consider V be the potential difference by one DC source across the combination of unknown resistances R₁ and R₂ [as shown in Fig. 1(b)].
Fig.1 (a) Two resistors AB and CD are placed one after the otherFig.1 (b) Two resistors AB and CD are connected in a series combination

If V₁ and V₂ be the potential differences measured by the voltmeter across each resistor, then
V = V₁ + V₂ ………(i)
According to Ohm’s law,
V₁ = IR₁, V₂ = IR₂
and V = IR_s ……..(ii)
where, R_s = Equivalent resistance of R₁ and R₂ in series combination.
From Eqs. (i) and (ii), we get
IR_s = IR₁ + IR₂
⇒ R_s = R₁ + R₂
Thus, the equivalent resistance of the series combination is equal to the sum of the individual resistances connected in the series circuit.

Procedure

• Note the least count and the zero error (if any) of the given ammeter and voltmeter.
• Clean the ends of connecting wires using a sand paper.
• Find the values of two given resistances R₁ and R₂ by the procedure given in Experiment 5.
  
  Fig. 2 (a) Circuit diagram of resistors in series

Fig. 2 (b) Block diagram of resistors in series

• Connect the resistances in series as shown in block diagram or circuit diagram given in Fig. 2.
• Put the plug in the key and take the readings of ammeter and voltmeter (as done in Experiment 5).
• Repeat the step 5 three times by changing the position of the sliding contact of the rheostat (as done in Experiment 5).
• Tabulate the readings and find the ratio of V and I. It will give the equivalent resistance of the combination.

Observation

• Least count of ammeter = …………. A
• Zero error of ammeter = ………… A
• Least count of voltmeter = ………… V
• Zero error of voltmeter = …………. V
• Zero correction in ammeter reading = ………. A
• Zero correction in voltmeter reading = ……… V

Calculations

• Mean value of R₁ = ………. Ω
• Mean value of R₂ = ……….. Ω
• Equivalent value of series combination,
  • By calculation, R’s = R₁ + R₂ = ………… Ω
  • By experiment, Rs = ………… Ω
    Difference in both values, Rs - R’s = ……… Ω

Result

• There is a close agreement between the calculated value and the value obtained by the experiment.
  Hence, Rs = R₁ + R₂ is verified.
• Equivalent resistance, Rs = …………. Ω

Percentage Error
It can be found by using the following relation:
Percentage Error


It shows that the percentage error is within the experimental error.

Precautions

• Remove the dust and other insulating particles from the ends of connecting wire, by rubbing it with sand paper.
• All the connections should be tight and properly done as per the circuit diagram.
• Take out the plug from the plug key in between the two observations.
• A low resistance rheostat should be used in the circuit to obtain a large variation in the current.
• The thick copper connecting wires should be used in the circuit.
• The positive terminal of the ammeter and voltmeter must be connected to the positive terminal of the battery or battery eliminator.
• Never connect the two terminals of the cell without any resistance.
• The pointers of the ammeter and voltmeter should be at zero mark when no current flows through them.
• Current should be passed through the circuit for a short time while taking observations; otherwise current would cause unnecessary heating in the circuit. Heating may change the resistance of resistors.
• The ammeter should be connected in series with the combination of resistors such that the current enters at the positive terminal and leaves at the negative terminal of the ammeter.
• Voltmeter should always be connected in parallel to the combination of resistors.

Sources of Error

• Reading error may be possible while observing the pointer of ammeter and voltmeter.
• Thick connecting wires may not be available at the time of performing the experiment.
• Area of cross-section of resistance may not be uniform across the length of the wire.
• The high resistance rheostat may be used.
• Current may be allowed for the longer period through the circuit.
• The terminal screws of the given instruments may not be tighten properly.