STUDY OF SERIES AND PARALLEL CIRCUITS
Object: -
To study the series and parallel circuits
APPARATUS: -
Sr. No. Name of Components Range No. Regd Remark
1.
2.
3.
4.
THEORY: -
SERIES CIRCUIT
When a number of resistances are connected in series the total resistance is the sum of all the resistance. In a series circuit same current flows all the resisters while the supply voltage gets divided across the resistors.
Resistance in Series
When some conductors having resistances R1, R2 and R3 etc. are joined end - on � end as in fig. , they are said to be connected in series. It can be proved that the equivalent resistance or total resistance between points A and D is equal to the sum of the three individual resistances:
Being a series circuit, it should be remembered that (i) current is the same through all the three conductors (ii) but voltage drop across each is different due to its different resistance and is given by Ohm�s Law and (iii) sum of the three voltage drops is equal to the voltage applied across the three conductors. There is a progressive fall in potential as go from point A to D as shown in fig.
? V = V1 + V2 + V3
= IR1 + IR2 + IR3 � (Ohm�s Law)
But V = IR
Where R is the equivalent resistance of the series combination.
? IR = IR1 + IR2 + IR3
Or
? R = R1 + R2 + R3
As seen from above, the main characteristics of a series circuits are:
1. Same current flows through all parts of the circuits.
2. Different resistors have their individual voltage drops.
3. Voltage drops are additive.
4. Applied voltage equals the sum of different voltage drops.
5. Resistances are additive.
6. Powers are additive.
PARALLEL CIRCUIT
In parallel circuits the reciprocal of the total resistance is equal to some of reciprocal of different resistance. The voltage across each branch of parallel to the circuits is equal to the supply voltages where as the current pass trough different branches may be different. In alighting system the lamps are connected in parallel so that each gets supply voltage of 230 volts.
Resistance in parallel
Three resistances, as joined in fig. are said to be connected in parallel. In this case (i) P.D. across all resistances is the same (ii) current in each resister is different and is given by Ohm�s Law and (iii) the total current is the sum of the three separate currents.
I = I1 + I2 + I3
= V/R1 + V/R2 + V/R3
Now, I = V/R
Where, V is the applied voltage
R = equivalent resistance of the parallel complication.
V/R = V/R1 + V/R2 + V/R3
Or
I/R = I/R1 + I/R2 + I/R3
The main characteristics of parallel circuits are:
1. Same voltage acts across all parts of the circuits.
2. Different resistors have their individual current.
3. Branch currents are additive.
4. Conductors are additive.
5. Powers are additive.
PROCEDURE: -
1. Set up connections a per circuit diagram.
2. Start supply and note down reading of voltmeter and Ammeter.
3. Then make calculations.
OBSERVATION TABLE AND CALCULATION
(A) FOR SERIES CIRCUIT: -
� Applied voltage (v) ������������.Volts.
� Current (I) ������������Amps.
� P.D. Across R1 = V1 ������������.Volts.
� P.D. Across R2 = V2 ������������.Volts.
� P.D. Across R3 = V3 ������������ Volts.
� Sum of P.D. voltage = V1 + V2 + V3
� Resistance R1 = V1 / I = �������.����.�Ohm.
� Resistance R2 = V2 / I = �������.�����.Ohm.
� Resistance R3 = V3 / I = �������.����� Ohm.
� Equivalent resistance of series circuits = V / I = 338.46 Ohm.
� Equivalent resistance of series circuit = R = R1 + R2 + R3 Ohm.
(B) FOR PARALLEL CIRCUIT: -
� Applied voltage (v) ������������ volts.
� Total Current (I) ������������ Amps.
� Branch current (I1) ������������ Amps.
� Branch current (I2) ������������ Amp.
� Sum of branch current I = I1 + I2 = ..�������� Amps.
� P.D. Across R1 (V1) ������������ volts.
� P.D. Across R2 (V2) ������������ volts.
� Equivalent resistance (R) = V / I = ��������� Ohm.
� Resistance (R1) = V1 / I2 =������������ Ohm.
� Resistance (R2) = V2 / I2 =������������ Ohm.
� Equivalent resistance 1 / R = 1 / R1 = 1 / R2.
CONCLUSION: FOR SERIES CIRCUITS: -
CONCLUSION: FOR PARALLEL CIRCUITS: -