Current & Voltage Through Series Resistors: Analysis of Series Circuits:
Before starting my tutorial on series-connected resistors, I would like to recall series circuits.
“Two elements connected in such a way that they share a single node exclusively.”
Similarly, two resistors are connected in series, when they share a single node exclusively.
Properties Of Series Connected Resistors:
- Current remains the same in every series-connected resistor
- Another property of the series circuit is the voltage division property. The voltage is divided proportionally to all resistors. The larger the resistance value, the greater will be the voltage drop across that resistance.
Formula Of Resistance In Series:
Apply Ohm's law to the circuits below,
Circuit 1:
The voltage drop across R1 is va
va = iR1
The voltage drop across R2 is vb
vb = iR2
The total voltage across circuit the is the sum of voltage drops across R1 and R2
v1 = va + vb … equation 1
Circuit 2:
Voltage across Req
v2 = iReq … equation 2
Observations and Calculations:
Have a close look at both circuits. v1 and v2 are the same that is 10V. I take same the same voltage sources, and the current flowing through the circuit remains the same. The difference is the number of resistances in the circuits. Circuit 1 has R1 and R2. and Circuit 2 has only Req.
Look at circuits 1 and 2,
v1 = v2
va + vb = v2
iR1 + iR2 = iReq
From observations and calculations, we can conclude that
Req = R1 + R2
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| Figure: Electrically equivalent circuits |
Implying that we can replace R1 and R2 with a single equivalent resistor. Similarly, we can replace N series resistors with a single equivalent resistor. This is because Req has the same voltage drop across terminals a & b. Also, current and power relationships in the equivalent circuit will remain the same.
The equivalent resistance of a series-connected resistor is the algebraic sum of all the individual resistances.
Req = R1 + R2 + R3 + …..RN
Analysis Of Some Confusing Series Circuits:
Circuit 1:
Circuit 1 is a series circuit. All 5 components are serially connected.
Circuit 2:
It is not a series circuit.
Circuit 3:
It is also a series circuit. It contains multiple sources and resistors. All are connected in series with each other.
Circuit 4:
It is not a series circuit.
Solved Examples:
Example 1:
A 12 V source is connected with these resistances: 1kΩ, 2kΩ and 4kΩ. How much current flows through the 4kΩ resistance?
Solution:
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| Figure: Draw the circuit with the help of given data |
| Before calculating the current, you have to find out the total or equivalent resistance of the circuit. After evaluating the total or equivalent resistance, apply Ohm's Law to find out the current through the circuit. |
The total resistance will be the sum of all individual resistances.
RT = R1 + R2 + R3
RT = (1+2+4) kΩ
RT = 7 kΩ
Current remains the same in a series circuit
Current through the 4kΩ is:
i = v/RT
i = 12/7
i = 1.7 mA
Example 2:
From the following data, evaluate the resistance value that should be connected in series to limit the load current to 5mA.
RL = load resistance = 250Ω
RS = series resistance =?
IT = total current required by the load resistance
First of all, draw a circuit and label it with the given data.
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| Figure: Circuit diagram for example 2 |
| RT = total resistance = RS + RL = RS + 250 |
RS = RT -250
IT = V/RT
5*10-3 = 5/RT
RT = 1000Ω
RS = 750Ω
Conclusion:
I discussed series-connected resistors in detail. As far as practical applications are concerned, resistors in series are frequently used to limit the voltage. Such circuits are called voltage divider circuits. In complex circuits, we frequently use this technique to simplify circuit analysis.
There is another way of solving series circuits without knowing the current values. This method is known as Voltage Divider Rule.
There is another way of solving series circuits without knowing the current values. This method is known as Voltage Divider Rule.
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