Combination Of Resistances

MATERIALS REQUIRED

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

THEORY

When two or more resistors are connected end to end, then they provide only one path to the flow of current i.e., the same current flow through each resistor. Then, they are in series combination.

V = V₁ + V₂

let v be the applied potential difference by a dc source across the combination of unknown resistors R₁ and R₂.

According to ohms law, for each resistor,

V₁ = IR₁, V₂ = IR₂

Then the equivalent resistance of the series combination of two resistors is given by

R_s = R₁ + R₂

Circuit Diagram

Apparatus Arrangement:

PROCEDURE

1. Join the circuit as shown in the circuit diagram or apparatus arrangement with one of the unknown resistors.

2. Find the values of two given unknown resistors R₁ and R₂ one by one.

3. Tabulate at least three readings of ammeter and voltmeter for the given unknown resistor.

4. By using Ohm’s law, find the value of each resistance.

5. Connect the given resistors in series combination between the terminals of voltmeter as shown in the figure above

6. Plug in the one - way plug key and note the readings of ammeter and voltmeter in the observation table.

7. Repeat the step 6 three times by changing the position of the sliding contact of the rheostat

OBSERVATION TABLE

OBSERVATIONS

1. Least count of ammeter:

The image of the ammeter is attached here:

The range of the ammeter =500 - 0 mA = 500 mA = 0.5 A

The number of divisions in between two consecutive values= 10

Therefore, the least count =

= 0.01 A

2. Zero error of ammeter:

The needle of the ammeter points towards zero of the main scale of the ammeter, therefore no zero error .

3. Least count of voltmeter:

The range of voltmeter = 2 - 0 V= 2 V.

The number of division in small scale between two division on the main scale

= 10

Therefore, the least count

4. Zero error of voltmeter = 0 V.

CALCULATIONS

1. Mean value of R₁ = 2.06 Ω

2. Mean value of R₂ = 4.06 Ω

Equivalent value of series combination:

(a) by calculation, = 2 Ω + 4 Ω = 6 Ω

(b) by experiment, = 5.99 Ω

RESULT

1. The calculated and the experimental value of equivalent resistance are similar. Hence R_s = R₁ + R₂ is verified.

2. The equivalent resistance, R_s = 5.99 Ω

PERCENTAGE ERROR

PRECAUTIONS

1. Remove the oxide layer from the ends of connecting wires by rubbing it with sandpaper.

2. All connections should be kept tight and properly done as per the circuit diagram.

3. Take out the plug from the plug key in between the two observations to avoid heating.

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.

MATERIALS REQUIRED

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

THEORY

An arrangement in which resistors are connected between two common ends of the circuit in such a way that the potential difference across each resistance is equal to the applied voltage, then such an arrangement is called the parallel combination

As shown in the figure, two resistances R₁ and R₂ are connected between two points A and B in the parallel combination.

Let the potential applied by the dc source to this combination be V. let I₁ and I₂ be the current measured by ammeters, connected in series with the resistor R₁ and R₂ respectively, then

I = I₁+I₂

According to ohms law, I₁ = V/R₁ and I₂ = V/R₂

If R_p, is the equivalent resistance of the given parallel combination having the same potential difference a the applied potential, then

or

Circuit Diagram

Apparatus Arrangement Diagram:

Connect all the resistors in parallel combination between the two terminals of the voltmeter as shown in the figure given below.

PROCEDURE

1. Connect the circuit as shown in the circuit diagram with one of the unknown resistors.

2. By using Ohm’s law, find the value of each resistance, Let it be R₁ or R₂.

3. Connect the given resistors in parallel combination between the two terminals of the voltmeter as shown in the circuit diagram above.

4. Plug in the key and take the readings of ammeter and voltmeter.

5. Repeat the step 5 for three times by changing the position of the sliding contact of the rheostat.

OBSERVATION TABLE

1. Least count of ammeter:

The image of the ammeter is attached here:

The range of the ammeter = 500 - 0 mA = 500 mA = 0.5 A

The number of divisions in between two consecutive values = 10

Therefore, the least count =

= 0.01 A

2. Zero error of ammeter:

The needle of the ammeter points towards zero of the main scale of the ammeter.

3. Least count of voltmeter:

The range of voltmeter = 2 - 0 V = 2 V.

The number of division in small scale between two division on the main scale

= 10

Therefore, the least count

4. Zero error of voltmeter = 0 V.

CALCULATIONS

1. Mean value of R₁ = 2.083 Ω

2. Mean value of R₂ = 1.973 Ω

Equivalent value of parallel combination:

(a) by calculation, R = 1 Ω

RESULT

1. The equivalent resistance of parallel combination = 1.08 Ω.

2. There is a direct agreement between the calculated value and the experimental value.

Hence, is verified.

PERCENTAGE ERROR

Percentage error

Percentage error = 8%

Precautions:

1. All the connection should be tight and properly done as per circuit diagram.

2. Take out the plug from the plug key in between the two observations.

3. A low resistance rheostat should be used in the circuit to obtain large variation in current.

4. A thick copper connecting wires should be used in the circuit.

5. The positive terminal of the ammeter and voltmeter must be connected with the positive terminal of the battery or battery eliminator.

If the pointer of the meter does not coincide with zero of the scale, this type of error in reading of the scale is called a Zero error.

The smallest value that can be measured accurately by an instrument is called its least count.

We will connect the ammeter or Voltmeter arbitrary in the circuit and observe the deflection of the pointer. If the deflection occurs in the opposite direction then by interchanging the terminal connection, we can use these devices.

If the deflection on ammeter goes beyond the full scale , we infer that:

1. The higher range ammeter has to be used to measure higher current.

2. The applied voltage is very high thus will require a high range voltmeter to measure applied voltage

It is advised to clean the ends of connecting wires to remove the insulating layer if any from to ends of the wire. Also, to remove any dust from the ends of the wire to ensure better flow of electrons in the junction.

Observed reading = Least count × Number of division

= 0.05 × 15

= 0.75 V

In series combination:

1. Current flowing across a different resistor connected in series are same

2. Voltage in a series is the sum of the voltage across the different resistor.

The equivalent resistance R_eq=R₁+R₂+…….+R_n.

The equivalent resistance in a parallel connection is given as:

In parallel combination:

1. The voltage across the resistor remains the same.

2. The current across the combination is the sum of the current across the different resistor.

The standard resistance coils are made up of manganin wire. The reasons are:

i. The variation of resistance with a rise in temperature is very less as compared to other metal.

ii. The resistivity of the material is very high & any resistance value can be made from it. Therefore, it is used as standard resistance.

1. The value of resistance should not change with time.

2. The value of resistance should almost remain the same with a change in temperature.

3. It should be convenient sizes.

The connecting wires are made of copper because copper has low resistivity and it conducts the current without offering much resistance.

The effective resistance in parallel combination is

That of series combination is R_s = 2R. Thus, we get R_s = 4R_p, i.e., equivalent resistance increases four times.

The resistor is a device which offers resistance, whereas resistance is the property of the resistor.

The household appliances should be connected in parallel in order to get equal voltage for each appliance and ensure that if one is a switch “on” or ”off,” others working are not affected.

The direction of current is from the positive terminal of the battery, it goes on through the components & then enters through negative terminal.

The current carriers are electrons and the motion of electrons is opposite from the electric current.

Ammeter is always connected in series with circuit as it should offer low resistance to the components added in the series. In this ways, the current can be measured accurately in low resistance.

Voltmeter should be connected in parallel because in parallel connection, the potential difference is same.

Voltmeter has very high resistance and ammeter has negligible resistance. This is because when voltmeter is connected in parallel across any two points, it will draw very less current (due to high resistance), hence it can measure the voltage accurately.

The closed path is necessary for electrons to move in a particular direction.

The resistance will decrease because the resistance has an in-direct relationship with the area.

Where, ρ is the constant (resistivity of the material)

Both copper and aluminium are good conductors of electricity, hence they are employed for electrical transmission.

The cell (battery eliminator) maintains the potential difference across a conductor.

In parallel connection, if one device fails to work, others will continue working as the potential difference across parallel connection is same.

In open circuit, no current can flow across the circuit. Whereas, in closed circuit, continuous current flows.