Series CircuitApplied Physics and Chemistry Circuit Lecture 3

Symbols Used

Series

Circuit in which current passes through all resistors

Only one path for current Each resistor uses up some of the potential

Vsource

= Va + V

b + ....

Resistance

Equivalent resistance (effective resistance) for devices in a series circuit is sum of individual resistances

R = R1 + R

2 + R

3 + …

Current

Current in a series circuit is the source voltage divided by the equivalent resistance

Current is the same everywhere in the circuit I

circuit = V

source/R

eq

Example

Two resistors, 47Ω and 82Ω, are connected in series across a 45V battery. What is the current in the circuit? What is the voltage drop at each resistor?

Known: R1=47Ω R

2=82Ω V=45V

Req

= R1 + R

2

Req

= 47Ω + 82Ω = 129Ω

Example Continued

Current in the resistor: I = V/R I = 45V/129Ω = 0.349 A Voltage at resistor 1: V = IR

V=(0.349 A)(47Ω) = 16.4 V Voltage at resistor 2: V = IR

V = (0.349 A)(82Ω) = 28.6 V

Example Continued

Will current increase, decrease or stay the same if the 47Ω resistor is replaced by a 37Ω resistor?

New Req

= 37Ω + 82Ω = 119 Ω

I = V/R = 45V/119Ω = 0.378 A Current increases

Example Continued

What is the new voltage drop at resistor 2? V = IR V = (0.378 A)(82Ω) = 31V

Series Circuit Uses

Series circuit can be used as a voltage divider

If a certain resistance needs a specific voltage, series circuit can be used to provide that

Example p 406

A 9.0 V battery and two resistors R1= 400 Ω and R2 = 500 Ω are connected as a voltage divider. What is the voltage across R2?

Parallel Circuits

Parallel Circuit

Multiple pathways for current Total current is the sum of the currents at each

resistor (Current is NOT the same everywhere) Potential difference is the same everywhere in

the circuit

Parallel Circuit

Equivalent resistance is reciprocal 1/R

eq = 1/R

1 + 1/R

2 + 1/R

3 …

Placing resistors in parallel always decreases the equivalent resistance of the circuit

Example

Three resistors, 60Ω, 30Ω, and 20Ω, are connected in parallel across a 90V battery. Find the current through each branch of the circuit. Find the equivalent resistance. Find the current through the battery.

Known: R1=60Ω R2=30Ω R3=20Ω V=90V

Example Continued

Current at R1: I=V/R I=90V/60Ω=1.5A Current at R2: I=V/R I=90V/30Ω=3 A Current at R3: I=V/R I=90V/20Ω=4.5 A Equivalent Resistance: 1/Req=1/60Ω + 1/30Ω +

1/20Ω = 6/60Ω Req = 10Ω

Total Current: I=V/R I=90V/10Ω I=9 A

Sample Circuits