CBSE Class 10 Science Practical Skills – Resistors in Parallel
BASIC BUILDING CONCEPTS
Parallel combination of resistors
The arrangement of resistors in which they are connected in such a way that their one end will be at higher potential and other end at lower potential is called parallel combination.
Characteristics of parallel combination
- Voltage across each resistor is same and is equal to the applied voltage.
- Current through each resistor is inversely proportional to the resistance of that resistor, i.e.
- Total current flowing in the circuit is the sum of the individual currents flowing in the different branches, i.e.,
- The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistance, i.e.
- The equivalent resistance is smaller than the least resistance used in the circuit, i.e.
Rp<R1, Rp<R2, Rp<R3……, etc
Therefore, due to the above characteristics of the parallel circuits, all the household electrical appliances are connected in a parallel combination.
Uses of parallel circuit
It is used when
- the resistance in the circuit is to be decreased.
- the current in the circuit is to be increased.
Therefore, for a household purpose, all electrical appliances are connected in parallel combination so that they get the same voltage from the power supply line and thus, work properly.
To determine the equivalent resistance of two resistors when connected in parallel.
Two standard resistance coils, ammeter, voltmeter, one-way plug key, a low resistance rheostat, connecting wires, battery or battery eliminator.
Parallel combination of resistors: An arrangement in which a number of resistors are connected between two common points in such a way that the potential difference across each resistor is equal to the applied voltage is called parallel combination of resistors.
If Rp is the equivalent resistance of the given parallel combination having the same potential difference as the applied potential, then 1/Rp=1/R1+1/R2 or Rp=R1R2/R1+R2
Connect all the resistors in parallel combination between the two terminals of the voltmeter as shown in the figure given below.
- Connect the circuit in the similar manner as shown in circuit diagram or apparatus arrangement with one of the unknown resistors.
- Find the values of two given unknown resistors R1 and R2 by adopting the procedure given in experiment 5 and record the observations in the observation table.
- Using Ohm’s law, find the value of each resistance. Let it be R1 or Rr
- Connect the given resistors in parallel combination between the two terminals of the voltmeter as shown in figure above.
- Put the plug in the key and take the readings of ammeter and voltmeter.
- Repeat step 5 three times by changing the position of the sliding contact of the rheostat.
- equivalent resistance of the combination.
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 of ammeter = ……..A
6. Zero correction of voltmeter = ……..V
- Mean value of Ry =……….. Ω
- Mean value of R2 =……….. Ω
Equivalent value of parallel combination:
- by calculation, Rp’ = R1R2/R1+R2 = ………… Ω
- by experiment, Rp =R1R2/R1+R2 = ………… Ω
- The equivalent resistance of parallel combination = ………… Ω
- There is a close agreement between the calculated value and the experimental value.
Hence,1/Rp=1/R1+1/R2 is verified
Percentage error = Experimental value – Calculated value /Calculated value = Rp-R’p/R’p ×100
SOURCE 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 resistor may not be uniform across the length of wire.
- There may be the use of high resistance rheostat.
- Current may be allowed for a longer period of time.
- The terminal screws of the instrument may not be tightened properly.
Which physical quantity remains the same in parallel combination: current or voltage?
Why does the total resistance decrease in a parallel combination?
In a parallel combination, the resultant cross-sectional area of conductor increases. Hence, the total resistance decreases.
How does the resistance depend upon the area of cross-section of the conductor?
It is inversely proportional to the area of cross-section of the wire, i.e. Rα 1/A
Can you distinguish between resistor and resistance?
A resistor is a device that offers resistance, whereas resistance, is the property of the resistor.
What is the direction of current sent by a cell?
The direction of current sent by a cell in the circuit is from positive terminal to negative terminal outside the cell.
How many times will the equivalent resistance of two identical resistors be increased if the parallel arrangement is changed to series arrangement?
The effective resistance of parallel combination is Rp = R/2and that of series is Rs = 2R
Therefore Rs = 4Rp , i.e. equivalent resistance increases four times.
Why is a voltmeter connected in parallel across the conductor?
To measure the maximum potential difference developed across the ends of a conductor, a high resistance device voltmeter is connected in parallel.
In what ratio the current divides itself in the parallel combination?
The current divides itself into the inverse ratio of the resistance, i.e. I α 1/R
Suppose in a combination, we find that the equivalent resistance is smaller than the smallest resistance used in the circuit. Which type of combination is present in the circuit?
It is a parallel combination.
Why is an ammeter connected in series in a circuit?
To measure the amount of electric current flowing in a circuit, ammeter is always connected in series with the circuit as it is a low resistance device.
What do you mean by the range of ammeter?
It is the maximum value of current which the ammeter can measure.
NCERT LAB MANUAL QUESTIONS
Two resistors having resistances of 4 Ω and 6 Ω respectively are connected in a circuit. It was found that the total resistance in the circuit is less than 4 Ω. In what way the resistances would have been connected?
According to the given condition, resistors of 4Ω and 6Ωare connected in parallel combination.
In parallel combination,
1/Rp=1/R1+1/R2 =1/4 +1/6=5/12
Therefore R = 2.4 Q
Two resistors are connected first in series and then in parallel. What effect will it have on the readings of voltmeter and ammeter?
There will be no change in the reading of voltmeter because applied voltage remains the same in both the cases but ammeter reading will be less in case of series combination as compared to parallel combination
of the same resistors because Rs > Rp and I α 1/R(for constant applied voltage) as shown in the following
In what way household appliances should be connected?
The household appliances should be connected in parallel in order to get equal voltage for each appliance and ensure that if one switch is ‘on’ or ‘off, others are not affected.
PRACTICAL BASED QUESTIONS
Multiple Choice Questions/VSA
For three circuits shown here,
the same two resistors R3 and R2 have been connected in parallel in all the circuits but the voltmeter and the ammeter have been connected in three different positions. The relation between the three voltmeter and ammeter readings would be [CBSE 2012, Delhi 2009]
(а) V1 = V2 = V3 and I1 = I2 = I3
(б) V1 ≠ V2≠ y3 and I1 = I2 = I3
(c) V1 = V2 = V3 and 11≠ I2 ≠I/3
(d) V1 ≠V2 ≠V3 and I1≠ I2≠ I3
Two students setup their circuits for finding the equivalent resistance of two resistors connected in parallel in two different ways as shown.
The circuit(s) likely to be labelled as correct
(a) are neither of the two circuits
(b) is only circuit I
(c) is only circuit II
(d) are both the circuits
In the experiment on finding the equivalent resistance of two resistors, connected in parallel, two students connected the ammeter in two different ways as shown in given circuits I and II. The ammeter has been correctly connected in
(a) circuit (I) only.
(b) circuit (II) only.
(c) both the circuits (I) and (II).
(d) neither of the two circuits.
A student did the experiment to find the equivalent resistance, of two given resistors, R] and R.v first when they are connected in series and next when they are connected in parallel. The two values of the equivalent resistance obtained by him were Rs and R respectively. He would find that
(a) Rs > Rs
(b) Rp > Rs
(c) Rs = Rp=(R1+R2/2)
(d) Rs = Rp but not equal to (R1+R2/2)
The voltmeter, ammeter and resistance in the circuit shown have been checked to be correct. On plugging the key, the ammeter reads 0.9 A, but the voltmeter reads zero. This could be because
(a) the range of the voltmeter is more than twice the battery voltage.
(b) the least count of the voltmeter is too high.
(c) the wires joined to the voltmeter terminals are loose.
(d) the voltmeter is incorrectly placed in the circuit.
On plugging the key, the voltmeter/ammeter is likely to be damaged in the circuit shown in figure
To determine the equivalent resistance of two resistors in parallel combination, a circuit is shown below. The component of the circuit whose terminals are wrongly connected is
In the experiment on finding the equivalent resistance of two resistors, connected in parallel, three students connected the voltmeter in their circuits, in the three ways, X, Y and Z as shown here.
The voltmeter has been correctly connected in
(a) cases X and Y only
(b) cases Y and Z only
(c) cases Z and X only
(d) all the three cases.
To determine the equivalent resistance of three resistors arranged in parallel, four students connected the resistors as shown in figures A, B,
C and D.
The correct set-up is that of student
The voltmeter, ammeter and resistance in the circuit shown have been checked and found to be correct. On plugging the key, the voltmeter reads 4.5 V, but the ammeter reads 1.5 A.
This could most likely be because the wires joined to
(а) the resistor R1 is loose.
(б) the resistor R2 is loose.
(c) both the resistors R1 and R2 are loose.
(d) the ammeter terminals are loose.
Out of the four circuits shown for studying the equivalent resistance of two resistor/resistors when connected in parallel, the correct sequence of procedure is
(a) (i), (ii), (iv) and (iii)
(b) (i), (iii) and (ii) only
(c) (iii), (i) and (ii) only
(d) (iv), (ii), (i) and (iii)
A student uses a battery of adjustable voltage 0-6 V. She has to perform an experiment to determine the equivalent resistance of two resistors when connected in parallel using two resistors of value 3 Ω and 6 Ω. The best choice of combination of voltmeter and ammeter to be used in the experiment is
(a) ammeter of range 0 – 5 A and voltmeter of range 0-10 V
(b) ammeter of range 0 – 5 A and voltmeter of range 0-5 V
(c) ammeter of range 0 – 2 A and voltmeter of range 0-10 V
(d) ammeter of range 0 – 5 A and voltmeter of range 0-2 V
You have two resistors R terminals marked a, b, c and d as shown.
In order to find the equivalent resistance of parallel combination of the two resistors f?1 and R2 how would you connect the terminals of the resistors Rr and R2 to the terminals X and Y in the circuit shown in the figure.
(a) X to a ; b to c and d to Y
(b) a and b both to X ; c and d both to Y
(c) a and c both to X ; b and d both to Y
(d) X to d ; c to b and a to Y
In the circuit shown below, the voltmeter and ammeter reading would be
(a) 3 V and 0.5 A
(b) IV and 3 A
(c) 3 V and 1A
(d) 3 V and 3 A
If a student while performing the experiment for finding the equivalent resistance of two resistors when connected in parallel keeps the circuit closed for a long time to measure the current and potential difference, then
(a) ammeter’s zero point will change.
(b) ammeter will show higher reading than the actual one.
(c) voltmeter will show higher reading than actual one.
(d) resistor will get heated up and its value will change.
The current ratio I1/I2 depends upon
(a)R1 and V
(b)R2 and V
(c)R1,R2 and V
(d)R1 and R2 only
Short Answer Questions
Draw a circuit diagram to show three resistors connected in parallel with a cell and a key. Write formula for the equivalent resistance R of this combination if the individual resistances of the resistors are Rx, R2 and R3.
Study the following circuit and answer the questions that follow:
(a) State the type of combination of the two resistors in the circuit.
(b) What will be the potential difference across the above combination if applied potential in 6 V?
In the circuit diagram given below, calculate:
(a) the total effective resistance of the circuit.
(b) the total current in the circuit.
List in a tabular form, two differences between a voltmeter and an ammeter.
To determine the equivalent resistance of two resistors Rj and R2 when connected in parallel, a student chooses the resistors to perform the experiment in such a way that Rx > R2. After taking observations, he plots the V-I graph for the same. Draw the same V-I graph as he plotted by taking ‘V’ on Y-axis and T on X-axis for
(i) R1 and R2, and
(ii) R1 and R2, and their equivalent resistance on
the same axis.
Give justification for both the cases.
Multiple Choice Questions/VSA
Short Answer Questions
2. (a) The circuit shows the parallel combination of the two resistors.
(b) The potential difference across the combination is 6 V because their one end is connected at higher potential and other end is at lower potential of the 6 V battery.
5. (i) The slope of V-I graph gives the resistance of the resistor used in the experiment. As Rj > R2, the slope for R, must be greater then the slope for R2.
(ii) In the parallel combination, the equivalent resistance is less than the least value resistance in the circuit. So in the V-I graph slope for parallel combination is less than that of R2.