## CBSE Class 10 Science Practical Skills – Resistors in Series

BASIC BUILDING CONCEPTS
Resistance: The property of a conductor which resists or opposes the flow of current through it is called the resistance of the conductor. Its SI unit is ohm(Ω).
Current ∝ 1/Resistance
The resistance of a uniform conductor is

1. directly proportional to the length of the conductor and
2.  inversely proportional to the area of cross-section of the conductor.
Therefore,          R∝ l/A  or R = ρ l/A

where p is the constant of proportionality, called the specific resistance or resistivity of the material of the conductor. It depends on the nature of the material of the conductor, i.e. it is constant for a particular material but different for different materials. The unit of resistivity is ohm-metre or Ω-m.

Series combination of resistors:
The arrangement in which various resistors are connected in such a way that they provide only one path to the flow of current is called the series combination of the resistors. The series combination of resistors Rv R2 and R3 is shown in the figure given below. CHARACTERISTICS OF SERIES CIRCUIT

1. The current flowing through all the resistors in series circuit is same.
2. The total voltage across the combination is equal to the sum of the voltage drop across the individual resistor.
3. Voltage across any resistor is directly proportional to the resistance of that resistor (as I is constant).
4.  Equivalent resistance of the series circuit is equal to the sum of the individual resistances, i.e. Req = R3 + R2 + R3.
5. The value of equivalent resistance is higher than the highest value of resistor used in the series circuit.

Uses of series circuit:
It is used when

1. the resistance of the circuit is to be increased.
2.  the current in the circuit is to be decreased.
3. the less potential difference across a particular resistor is needed.

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

MATERIALS REQUIRED
Two standard resistance coils, ammeter, voltmeter, one-way plug key, low resistance rheostat, connecting wires, cell or battery eliminator.

THEORY
Series combination of resistors: The end to end connection of two or more resistors are said to be in series combination if they provide only one path to the flow of current, i.e. same current would flow through each resistor.
The equivalent resistance of the series combination of two resistors is given by
Rs = R1 + R2

Circuit Diagram Assembly Diagram PROCEDURE

1. Connect the circuit in the similar manner as shown in circuit diagram or apparatus arrangement with one of the unknown resistors.
2.  Find the values of two given unknown resistors R1 and R2 by adopting the procedure of Experiment 5 and record the observations in observation table.
3.  Using Ohm’s law, find the value of each resistance. Let it be R1 and R,2.
4. Connect the two given resistors in series combination across the terminals of voltmeter as shown in figure above.
5.  Put the plug in the key and take the readings of ammeter and voltmeter.
6. Repeat step 5 three times by changing the position of the sliding contact of the rheostat.
7. Tabulate the readings and find the ratio of V and I for the series combination. It will give the equivalent resistance of the combination.

OBSERVATION TABLE OBSERVATIONS

1.  Least count of ammeter = …………. A
2.  Zero error of ammeter =…………. A
3. Least count of voltmeter=………….V
4. Zero error of voltmeter = ………….V
5. Zero correction in ammeter reading = A
6.  Zero correction in voltmeter reading = V

CALCULATIONS

1. Mean value of  R1 = ……………Ω
2. Mean value of R2 = ……………Ω

Equivalent value of series combination

1. by calculation R’s = R1 + R0 =……………Ω.
2.  by experiment, R . =……………Ω
Difference in both values = Rs-R’s =……………Ω

RESULT

1.  There is a close agreement between the calculated and the experimental values of equivalent resistance. Hence, Rs = R1 + R2 is verified.
2. The equivalent resistance, Rs = ……………Ω

PERCENTAGE ERROR
Percentage error =Experimental value – Calculated value /Calculated value =Rs-R’s/R’s  100 =……………..%

PRECAUTIONS

1. Remove the dust and other insulating particles from the ends of connecting wires by rubbing it with a sand paper.
2. All the connections should be kept tight and properly connected as per circuit diagram.
3. Take out the plug from the plug key in between the two observations.
4. A low resistance rheostat should be used in the circuit to obtain a large variation in current.
5. A thick copper connecting wire should be used in the circuit.
6. The positive terminals of the ammeter and voltmeter must be connected to the positive terminal of the battery or battery eliminator.
7. The voltmeter should be connected in parallel to the combination of resistors.
8. Never connect the two terminals of the cell without any resistance.

SOURCE OF ERROR

1. Reading error may be possible while observing the pointer of ammeter and voltmeter.
2. Thick connecting wires may not be available at the time of performing the experiment.
3. Area of cross-section of resistance may not be uniform across the length of wire.
4. There may be the use of high resistance rheostat.
5. Current may be allowed for a longer period of time.
6. The terminal screws of the instrument may not be tightened properly.

INTERACTIVE SESSION

Question 1:
How will you find the equivalent resistance when resistors are connected in series?
The equivalent resistance of two resistors R1 and R2 is determined by Rs = R1 + R2

Question 2:
When do we put the resistors in series combination?
Whenever we need the higher value of resistance, we put the resistors smaller value in series.

Question 3:
What is the relationship between V and R for the series combination?
Voltage across any resistance is directly proportional to the resistance of that resistor.

Question 4:
Which one is same in series, current or voltage?
Current remains the same in each resistor. .

Question 5:
When two resistors of unequal resistances are connected in series, what will be the potential difference across each resistor?
Potential difference across each resistor will be different.

Question 6:
Why are the standard resistances made of manganin?
Because there is a negligible change in the resistance of manganin wire with change in temperature.

Question 7:
Why are the connecting wires made of copper?
Because copper metal has low resistivity and it conducts the current without offering much resistance.

Question 8:
What should be the characteristics of standard resistance?
(i) The value of resistance should not change with the passage of time.
(ii) The value of resistance should almost remain the same with change in temperature.
(iii) It should be of convenient size.

Question 9:
Why resistance becomes more in series combination?
The effective length of all the resistors in series combination increases. Hence, equivalent resistance of the combination increases as Rα l.

Question 10:
What is the use of rheostat in the circuit?
It is used to change the current in the circuit which can be done by changing the sliding contact of the rheostat.

NCERT LAB MANUAL QUESTIONS

Question 1:
If two resistors having resistances of 2 Q and 4 Q respectively are connected in a series combination in an electric circuit, what will be the net resistance in the circuit?
The net resistance in a series combination in an electric circuit is given by
RS=R1+R2 = 2Ω + 4Ω = 6Ω

Question 2:
In an electric circuit, a resistor of 5 11 resistance is connected to a battery of 5 V through an ammeter and a plug key. Now, in this circuit, an another resistor of 10 Q resistance is connected in series with 5 Q resistor. Will there be any change in the ammeter reading? How much?
The reading of ammeter when 5 Q resistor is connected in the electric circuit is Question 3:
In the above question, what is the potential difference across the two ends of the resistor of 5Vresistance, when it is alone in the circuit? What is the potential difference across the two ends of resistor of 5 Ωresistance when it is connected in series with the resistor of 10Ωresistance? What is the potential difference across the series combination?
The potential difference across the two ends of the resistor of 5Ω resistance when it is alone in the circuit is PRACTICAL BASED QUESTIONS
Multiple Choice Questions/VSA

Question 1:
The values of resistances marked on the coils RI and R2 are found to be correct. A student connects the given resistors in the following manner: He then connects the terminals marked X and Y above to the terminals marked X and Y in the circuit. The average value of the ratio V/l in the observations recorded in the circuit would be
(a) 9 Q
(6) 6 1)
(c) 3 Q
(d) 2 11

Question 2:
Observe the figures K, L, M, N given here.  The correct way of connecting the ammeter and voltmeter with a series combination of two resistors in a circuit for finding their equivalent resistance, is shown in diagram
(a) K
(b) L
(c) M
(d) N

Question 3:
A student sets up an electric circuit shown here for finding the equivalent resistance of two resistors in series. In this circuit, the (a)resistors have been connected correctly but the voltmeter has been wrongly connected.
(b)resistors have been connected correctly but the ammeter has been wrongly connected.
(c)resistors as well as the voltmeter have been wrongly connected.
(d)resistors as well as the ammeter have been wrongly connected.

Question 4:
Out of the two circuits shown here, the two resistors f?1 and R2 have been correctly connected in series in (a) circuit A only
(b)circuit B only
(c)both circuits A and B
(d) neither of the two circuits

Question 5:
In the experiment on finding the equivalent resistance of two resistors connected in series, the ammeter is correctly connected in (a) circuit (I) only
(b) circuit (II) only
(c) both circuits (I) and (II)
(d) neither of the two circuits.

Question 6:
Students A and B connect the two resistors R1 and R2 given to them in the manner shown below, and then insert them at X and Y into the measuring circuit shown below. (a) Both students will determine the equivalent resistance of the series combination of R1 and R 2
(b) Both students will determine the equivalent resistance of parallel combination of R1 and R2
(c) Student A will determine the equivalent resistance of series combination while B determines the equivalent resistance of parallel combination
(d) Student A will determine the equivalent resistance of parallel combination while B determines the equivalent resistance of series combination

Question 7:
For the circuits shown in figures I and II, the voltmeter reading in both the circuit would be (a) 5 V, 5 V
(b) 2 V, 3 V
(c) 1 V, 5 V
(d) 3 V, 2 V

Question 8:
To determine the equivalent resistance of two resistors when connected in series, a student arranged the circuit components as shown in the diagram. But he did not succeed to achieve the objective. Which of the followings mistakes has been committed by him in setting up the circuit?
(a) Position of voltmeter is incorrect
(b) Position of ammeter is incorrect
(c) Terminals of voltmeter are wrongly connected
(d) Terminals of ammeter are wrongly connected

Question 9:
A student has to connect 4 cells of 1.5 V each, to form a battery of voltage 6 V.The correct way of connecting these cells is shown in figure (a) A
(b) B
(c) C
(d) D

Question 10:
While doing their experiment, on finding the equivalent resistance of two resistors connected in series, three students A, B, C set up their circuits as shown here The correct set-up is that of
(a) students A and B
(b) students B and C
(c) students C and A
(d) all the three students

Question 11:
The diagram shows a network of four resistors which are connected to an electric source. Identify the resistors which are connected in series in this network. (a) B, A and £>
(b) B, C and D
(c) C, D and A
(d) A, B and C

Question 12:
The given circuit diagram shows the experimental arrangement of different circuit components for determination of equivalent resistance of two resistors connected in series. The components X, Y and Z shown in the circuit, respectively, represent.
(a) rheostat, resistor, ammeter
(b) ammeter, voltmeter, rheostat
(c) voltmeter, ammeter, rheostat
(d) rheostat, ammeter, voltmeter

Question 13:
In their experiment, on finding the value of j equivalent resistance of two resistors connected in series, three students connected the ammeter, in their circuits, in the three ways X, Y and Z shown below. Assuming the ammeters to be ideal, the ammeter has been incorrectly connected in
(a) case X only
(b) case Y only
(c) case Z only
(d) All the three cases

Question 14:
The following instruments are available in a laboratory:
Milliammeter A1 of range 0 – 300 mA and least count 10 mA
Milliammeter A2 of range 0 – 200 mA and least count 20 mA
Voltmeter V1 of range 0 – 5 V and least count 0. 2 V
Voltmeter V2 of range 0 – 3 V and least count 0.3 V
Out of the following pairs of instruments, which pair would be the best choice for carrying out the experiment to determine the equivalent resistance of two resistors connected in series?
(а) Milliammeter A1 and voltmeter V1,
(б) Milliammeter A2 and voltmeter V2
(c) Milliammeter A1 and voltmeter V2
(d) Milliammeter A2 and voltmeter V1,

Question 15:
For determining the equivalent resistance of two resistors R1 and R2 connected in series, three students X, Y and Z set up their circuits as shown below. The correct set-up is that of
(a) student X only
(b) student Y only
(c) student Z only
(d) students X and Z

Question 16:
Study the I-V graph for the conductors A, B and C having resistance RA, RB and R(„ If conductors A and B are connected in series, then slope of equivalent resistance would be (а) less than that of A
(б) more than that of A
(c) equal to slop of B
(d) equal to slope of C

Question 17:
Two students perform experiments on two given resistors R1 and R,2 and plot the V-I graph shown by diagram 1 and 2 for A, > R,„ the diagrams correctly represents the situation on the plotted curves is (a) diagram 1
(b) diagram 2
(c) both
(d) neither 1 nor 2

Question 1:

1.  Draw a schematic diagram of a circuit consisting of a cell of 1.5 V, 10 Q and 15 Q resistor and a plug key all connected in series.
2. Which one is same in series, current or voltage?

Question 2:
Resistance of three resistors are given as R1 = 10 Q, R2 = 20 Q and R3 = 30 Q. Calculate the effective resistance when they are connected in series. Also calculate the current flowing when the combination is connected to a 6 V battery.

Question 3:
A student has three voltmeters across three resistances R,, R2 and R3 as shown in the circuit,  Given that Rx < R2 < R3

1. Write V1,V2, and V3 in decreasing order of the reading shown by j each of them,
2. What will you observe about the potential difference across the series the series combination? Question 4:
How will you connect a given set of resistors so that the equivalent resistance is increased? Give reason for your answer.

Question 5:

Multiple Choice Questions /VSA

1. (a)
2. (b)
3. (a)
4. (a)
5. (c)
6. (a)
7. (a)
8. (cl)
9. (a)
10. (b)
11. (b)
12. (b)
13. (c)
14. (a)
15. (d)
16. (a)
17. (a)

1. (ii) Current remains the same in a series circuit.

2.Effective resistance of series combination is given by 3.

1.  As V=IR
For the same current in series combination
V∝I
R1<R2<R3, we get V1<V2<V3
2. We observe that in a series combination, the potential difference V is equal to the sum of potential difference V1, V2 and V3, that is
V = Vr + V2 + V8.

4.All the given set of resistors must be connected in series so that the equivalent resistance is increased.
Reason: The effective length of all the resistors in the series combination increases. Hence, equivalent resistance of the combination increases as R oc l.

5.Advantage of series combination: Batteries are connected in series combination to get higher voltage.
Disadvantage of series combination: In series arrangement, when one compohent fails, the circuit is broken and none of the components works.