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.IT = I1 = I2 = I3 = ... = In

 Circuit 1 IT = Total current IR1 = Current through resistor R1 IR2 = Current through resistor R2 In a series circuit, all  currents are the same: IR1 = IR2 = IT Circuit 2 IT = Total current IR1 = Current through resistor R1 IR2 = Current through resistor R2 IR3 = Current through resistor R3 In a series circuit, all  currents are the same: IR1 = IR2 = IR3 = IT

 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 RT = R1 + R2 + R3 = 81 + 82 + 98 = 261W Step 2: Use Ohm's Law to calculate the total current
 IT = VT = 15.8 =  0.0605 = 60.5mA RT 261

Step 3: Determine the current for each resistor

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

IR1 = IR2 = IR3 = IT

And because IT = 60.5 mA,

IR1 = 60.5 mA,
IR2 = 60.5 mA
IR3 = 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:

IR1 = IR2 = IR3 = IT = 60.5mA

VR1 = IR1 R1 = 60.5mA x 81W = 4.9 V

VR2 = IR2R2 = 60.5mA x 82W = 5 V

VR3 = IR3R3 = 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. VT = V1 + V2 +V3 + ... + Vn

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