Basic Electric CircuitsChapter 18

Circuit Components

Series Circuits

Series CircuitsThe current supplied is not

allowed to branch. It flows through a single loop.

Voltages – The sum of the voltage across the entire loop is zero

Current – Remains the same through all components

This Means That…Voltage

◦VT = V1 + V2 + V3

Current◦I1 = I2 = I3

Series CircuitsVoltage means change in

electrical potential, so voltage gains and losses are represented by +/- signs, respectively.

For a circuit, the individual voltages across resistors add to equal the voltage across the battery terminals.

Series CircuitsEach resistor in series must carry

the same current because charge can’t pile up or leak out at any location in the circuit.

Restated: When resistors are connected in series, the current must be the same through all the resistors.

Series Circuits

Series CircuitsEquivalent series resistance (RS)

is defined as the resistance value of a single resistor that could replace the actual resistors and yet maintain the same current.

RS = R1 + R2 + R3 + … + Rn

Parallel Circuits

Parallel CircuitsThe current branches and then

rejoins later.Multiple loops

Voltages – The voltage across each resistor must be the same

Current – The current divides into different paths and then rejoins later

This Means That…Voltage

◦V1 = V2 = V3

Current◦IT = I1 + I2 + I3

Parallel CircuitsIf each resistor in parallel is equal,

then the current across each will be equal. This is generally not the case.

Current divides across the resistors so that the larges current will take the path of least resistance.

However, no one resistor will take all of the current.

Parallel Circuits

Parallel CircuitsEquivalent Parallel Resistance is

the value of a single resistor that could replace all the resistors and maintain the same current.

Parallel CircuitsThe equivalent resistance of

resistors in parallel is always less than the smallest resistance in the arrangement.

ExampleWhat is the equivalent resistance

of three resistors (1Ω, 2Ω, 3Ω) when connected (a) in series (b) in parallel? (c) How much total current will be delivered by a 12 Volt battery in each of these arrangements? (d) How much current will be in each resistor and what is the voltage drop across each resistor in each of these arrangements?

Example (Conceptual)Consider a string of Christmas

tree lights composed of bulbs with jumper shunts. If the filament of one bulb burns out and the shunt completes the circuit, will the other bulbs each (a) glow a little more brightly, (b) glow a little more dimly, or (c ) be unaffected?