Resistors Circuits
1. Series Connection
Here, we have three Resistors (labeled R1, R2, and R3) connected in a long chain from one terminal of the battery to the other. (It should be noted that the subscript labeling—those little numbers to the lower-right of the letter “R”—are unrelated to the resistor values in ohms. They serve only to identify one resistor from another.)
The defining characteristic of a series circuit is that there is only one path for current to flow. In this circuit, the current flows in a clockwise direction, from point 1 to point 2 to point 3 to point 4 and back to around 1.
Since current across each resistor is same and equal to total current flow in the circuit that is I.
If we calculate the voltage drop of each 1 resistor of them, by using Ohm's law.
Voltage across resistor R1, V1 = I R1 ..........(1)
Voltage across resistor R2, V2 = I R2 .........(2)
Voltage across resistor R3, V3 = I R3 ..........(3)
Voltage drop across whole circuit, V = Voltage drop across resistor R1 + voltage across resistor R2 + voltage drop across resistor R3
That is V = I R1 + I R2 + I R3 = I ( R1+ R2 + R3 )
or V/I = R1 + R2 + R3 ..........(4)
And according to ohm's low V/I givis the whole circuit resistance, we can say
V/I = R
From the above discussion for a series circuit we conclude that.
1. Same current flows through all parts of
the circuit.
2. Applied voltage is equal to the
sum of voltage drops across the different parts of the circuit.
3. Different resistors have their
individual voltage drops.
4. Voltage drop across individual
resistor is directly proportional to its resistance, current being the same in
each resistor.
5. Voltage drops are additive,
6. Resistances are additive,
7. Powers are additive. Series circuits are common in electrical equipment. The tube filaments small radios usually in series. Current controlling devices are wired in series with the controlled equipment. Fuses are in series with the equipment they protect. A thermostat switch is in series with the heating element in an electric iron. Automatic house-heating equipment has a thermostat, electromagnet coils, and safety cut-outs in series with a voltage source. Rheostats are placed in series with the coils in large motors for motor current control.
For an Example. If we put the value of that resistors and voltage source and then calculate the voltage drop between each resistor and total voltage drop.
V = I (5+10+12)
V = I×R1, .....(i)
V = I×R2 ......(ii)
V = I×R3 .....(iii)
V = I×R1 + I×R2 + I×R3 ....(1)
V = .89×5 + .89×10 + .89×12
V = 4.45+8.9+10.68
V= 24.0
V= 24 V Ans.
2. Parallel Connection
When a number of Resistors are connected in
such a way that one end of each of them is joined to a common point and the
other end being joined to another common point, as shown in image then resistor
are said to be connected in parallel and such circuits are known as parallel
circuits . In these circuits current is divided into as many paths as the
number of Resistors.
Let the Resistors R1, R2, and R3 be
connected in parallel, as shown in image and the potential difference of V
volts be applied across the circuit.
Since voltage across each resistor is same
and equal to voltage applied to the circuit that is V.
According to Ohm's law
Current in resistor R1, I1 =
V/ R1 ..........(1)
Current in resistor R2, I2 =
V/R2 .........(2)
Current in resistor R3, I3 =
V/R3 ..........(3)
Adding eqs. 1, 2 and 3 which we
have.
I1 + I2+ I3 = V/ R1 + V/R2 + V/R3 = V( 1/ R1 + V/R2 + V/R3)
And since I1 + I2 +I3 = I, the total
current flowing through the circuit.
I = I1 + I2 + I3 = V( 1/ R1 + V/R2 + V/R3)
I/V = 1/ R1 + V/R2 + V/R3
And I/V = 1/R where R is the equivalent
resistance of the whole circuit.
1/R = 1/ R1 + 1/R2 + 1/R3
Thus when a number of resistor are connected in parallel, the reciprocal of the equivalent resistance is given by the arithmetic sum of the reciprocal of their individual resistances.
1/R = 1/ R1 + 1/R2 + 1/R3
Also G = G1 + G2 + G3
where 1/R = G
R = 1/G
From the above discussion for a parallel
circuit we conclude that.
1. Same voltage acts across all parts
of the circuit.
2. Different resistors (or branches)
have their individual currents.
3. Total circuit current is equal to the
sum of individual currents through the various resistors (or branches).
4. Branch currents are additive.
5. Conductance’s are additive,
6. Powers are additive.
7. The reciprocal of the equivalent or combined resistance is equal to the sum of the reciprocals of the resistances of the individual branches. Parallel circuits are very common in use. Various lamps and appliances in a house are connected in parallel, so that each one can be operated independently. A series circuit is an "all or none" circuit, either every thing operates or nothing operates. For individual control, devices are wired in parallel.
In next post i will introduce about 'conductivity'.
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