Basic Electric Circuits Chapter 18

Circuit Components

Series Circuits

The 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 ◦ V T = V 1 + V 2 + V 3 Current ◦ I 1 = I 2 = I 3

Series Circuits Voltage 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 Circuits Each 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

Equivalent series resistance (R S ) is defined as the resistance value of a single resistor that could replace the actual resistors and yet maintain the same current. R S = R 1 + R 2 + R 3 + … + R n

Parallel Circuits

The 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 ◦ V 1 = V 2 = V 3 Current ◦ I T = I 1 + I 2 + I 3

Parallel Circuits If 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

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

Parallel Circuits The equivalent resistance of resistors in parallel is always less than the smallest resistance in the arrangement.

Example What is the equivalent resistance of three resistors (1 Ω, 2 Ω, 3 Ω ) 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?