Free-Ed: Basic Electronics Fundamentals

Basic Circuit Analysis
Series Circuits

Section 1-3 Kirchhoff's Voltage Law

Important Fact

The current in a series circuit is the same through each component and equal to the total current.

I_T = I₁ = I₂ = I₃ = ... = I_n

Circuit 1

I_T = Total current

I_R1 = Current through resistor R₁

I_R2 = Current through resistor R₂

In a series circuit, all currents are the same:

I_R1 = I_R2 = I_T

Circuit 2

I_T = Total current

I_R1 = Current through resistor R₁

I_R2 = Current through resistor R₂

I_R3 = Current through resistor R₃

In a series circuit, all currents are the same:

I_R1 = I_R2 = I_R3 = I_T

This is an example of a very general type of series circuit -- not just a battery and three resistors connected in series. We don't know exactly what the Source is. It might be a battery, an electrical generator, or any other source of electrical energy. Likewise the loads aren't necessarily resistors. They might be lamps, electronic equipment, or any other appliance that presents a fixed resistive load.

The important point is that the ammeter (A) is reading 2.8 A. This is a series circuit, so you can be confident that the source is driving the circuit with 2.8 A, and that the same amount of current is flowing through each of the loads.

Calculating the Currents for Series Resistor Circuits

Important Fact

When you know the total voltage and total resistance for a series resistor circuit, you can use Ohm's Law to calculate the total current (and hence the current through each of the resistors).

Example

This series resistor circuit has a DC source that measures 15.8V, and resistors having the values shown on the diagram. Your task is to calculate the total current (IT) and the current through each of the resistors.

Step 1: Calculate the total resistance of the circuit

R_T = R₁ + R₂ + R₃ = 81 + 82 + 98 = 261W

Step 2: Use Ohm's Law to calculate the total current

I_T = V_T = 15.8 = 0.0605 = 60.5mA

R_T 261

Step 3: Determine the current for each resistor

It is a property of series circuits that all currents are equal, so

I_R1 = I_R2 = I_R3 = I_T

And because I_T = 60.5 mA,

I_R1 = 60.5 mA,

I_R2 = 60.5 mA

I_R3 = 60.5 mA

More Examples

Calculating the Voltages for Series Resistor Circuits

You have been seeing how it is possible to determine the total resistance and total current for a series circuit.

Important Fact

When you know the resistance and current for all resistors in a series circuit, you can use Ohm's Law to calculate the voltage for each resistor.

Example

In an earlier example, you calculated the total current through a series resistor circuit on the basis of the applied voltage VT and the total resistance of the circuit RT:

I_R1 = I_R2 = I_R3 = I_T = 60.5mA

V_R1 = I_R1 R₁ = 60.5mA x 81W = 4.9 V

V_R2 = IR₂R₂ = 60.5mA x 82W = 5 V

V_R3 = I_R3R₃ = 60.5mA x 98W = 5.9 V

VR1 = 4.9 V

VR2 = 5 V

VR3 = 5.9 V

Important Fact

The sum of voltages across each resistor in a series circuit is equal to the total voltage.

V_T = V₁ + V₂ +V₃ + ... + V_n

Examples and Exercises

Determine the values requested for this series circuit. Round answers to one decimal place.

Some Facts About Current and Voltage in Series Circuits

1. Removing a resistor from a series circuit:

Raises raises the total resistance to infinity
Drops the total current to zero
Causes the total source voltage to appear across the point where the resistor was removed

2. Shorting a resistor in a series circuit

Decreases the total resistance.
Increases the total current
Causes 0V to appears across the shorted component