Chapter 20Circuits

AndCircuit Elements

20.1 Schematic Diagrams and Circuits

Objectives1. Interpret and construct circuit diagrams

2. Identify circuits as open or closed

3. Deduce the potential difference across a circuit load, given the potential difference across the battery’s terminals

…is a graphic representation of anelectric circuit, with standardizedsymbols representing circuitcomponents (aka, circuit diagram)

Schematic Diagram

Circuit Elements and Symbols

Draw the schematic for this circuit

Interpret the circuit elements in this schematic

Electric Circuit

…a set of electrical componentsconnected so that they provideone or more complete paths forthe movement of charges (i.e.,paths for current to flow)

Circuit Definitions

Load – any element or group of elements in a circuit that dissipates energy

Open circuit – incomplete path in a circuit, resulting in no current flow

Closed circuit – a closed loop path exits in which current can flow

Short circuit – a circuit without a load, so there is very little (essentially none) resistance to current

emf – the energy per unit charge supplied by a source of electric current. Any device that increases the potential energy of the charges in a circuit is a source of emf.

A couple more definitions….

Battery terminal voltage – is slightly less than emf due to the battery’s internal resistance (from charges colliding with atoms as they move from one terminal to the other inside the battery)

emf versus terminal voltage

The emf () is the “ideal”voltage available fromthe battery. The terminalvoltage (Vt) is the actual maximum voltage availablefrom the battery, which is Slightly less than emf due tothe internal resistance (r) ofthe battery.

Conservation of Energy in a Circuit

Inside the battery – the chemical energy of the battery is converted to electrical potential energy of the chargeOutside the battery – the charge’s electrical potentialenergy is converted to other forms of energy (light, heat)Conservation of energy – the charge must gain as muchas it loses in one complete trip around the circuit

20.2 Resistors in Series or in Parallel

Objectives1. Calculate the equivalent resistance (Req)

for a circuit of resistors in series, and find the current and potential difference across

each resistor in the circuit.

2. Calculate the equivalent resistance (Req) for a circuit of resistors in parallel, and find the current and potential difference across each resistor in the circuit.

Series – describes a circuit or portion of a circuit that provides a single conducting path without junctions

Parallel – describes two or more components in a circuit that are connected across common points or junctions, providing separate conducting paths for the current

Series vs Parallel

Series Circuit Parallel Circuit

Calculations for Resistors in Series

Resistors in series all have the same current running through them

ΔV = ΔV1 + ΔV2 + ΔV3…. and ΔV = IR

So, ΔV = IR1 + IR2 + IR3… but I is the same

So, IReq = I(R1 + R2 + R3)…. which becomes

Req = R1 + R2 + R3…

Calculations for Resistors in Parallel

Resistors in parallel all have the same potential difference across them

Ieq = I1 + I2 + I3… and I = ΔV / R

So, ΔVeq = ΔV/R1 + ΔV/R2 + ΔV/R3 …

But ΔV is the same, so…

1/Req = 1/R1 + 1/R2 + 1/R3

Facts: Series vs Parallel Resistors

Req for resistors in series is always greater than any individual resistance in the circuit

Req for resistors in parallel is always less than the smallest resistance in the circuitSeries circuits require all elements to conductParallel circuits do not require all elements to conduct

SERIES PARALLELReq = R1 + R2 + R3 + … 1/Req = 1/R1 + 1/R2 + 1/R3 +

…I is constant around the circuit, so I is the same at each resistor

It = IR1 = IR2 = IR3

I across each resistor is different (assuming different R’s) and the total current is

It = IR1 + IR2 + IR3 + …

ΔV is different across each resistor (assuming different R’s) and the total potential difference is

ΔVtotal = VR1+VR2+VR3+… = ΔVsource

ΔV is the same across each resistor

Vsource =VR1=VR2=VR3

Questions

1. A 9.0V battery is connected in series to four light bulbs having resistances of 2.0Ω, 4.0Ω, 5.0Ω and 7.0Ω.

a) Draw circuitb) What is Req ?c) What is I?

2. The same light bulbs from problem #1 are now connected in parallel to the 9.0V battery.

a) Draw circuitb) What is Req?c) What is I?

Answers

1. a) Req = 18.0 Ωb) I = 0.50 A

2. a) Req = 0.917 Ω b) I = 9.8 A

20.3 Complex Resistor Combinations

Objectives1. Calculate the equivalent resistance for a complex circuit involving both series and parallel portions

2. Calculate the current in and the potential difference across individual elements within a complex circuit

Complex Circuits

Combination of some resistors in series and some resistors in parallel

Calculating Req and I for a Complex Circuit

What is Req for this circuit?What is I?

Answers

Req = 60 Ω I = 2 A

Calculating I and ΔV Across an Individual Resistor in a Complex Circuit

What is I at R4?What is ΔV across R4?

Answers

I at R4 = 1.5 AΔV across R4 = 22.5 V

Complex Circuit Example

a) Req = ?b) It = ?

c) V across 2.0 resistor = ?d) I in 4.0 resistor = ?

Solving Complex Circuits with Kirchoff’s Rules

1. The sum of the currents entering any junction must equal the sum of the currents leaving that junction.

2. The sum of the potential differences (ΔV’s) around any closed circuit loop must be zero.

Kirchoff’s Rules Approach

1. Choose a junction and draw your current arrows in and out of the junction2. Choose your voltage loops (need to use 1 less loop than the total number of loops), and choose the direction of current flow in each loop

3. Write out your junction and loop equations in terms of current.

4. Solve for the unknown currents in all equations

5. If any or your currents end up negative, then their direction is opposite of what you chose

Adding or Subtracting in the Voltage Loops for Kirchoff’s Rules

1. Choose a loop direction

2. If your loop direction is the same as the conventional current as you cross a battery, then ADD the ΔV

3. If your loop direction is the same as conventional current as you cross a resistor, then SUBTRACT IR

4. If your loop direction is opposite the conventional current as you cross a resistor then ADD IR

Use Kirchoff’s Rules

Let’s use this junction for Rule #1

Let’s use these 2 loops for Rule #2

Measuring Resistance (R)

To measure resistance, the resistor must not be attached to an active circuit (i.e., no current can be flowing throughthe resistor).

On the meter, the black plug goes to COM, the red plug goes to and the dial must be set to . Sometimes there are multiple scales for . Choose the appropriate scale to provide the most precise resistance measurement.

Measuring Current (I)

To measure current, thecurrent must flow throughthe meter, therefore themeter has to be connectedin series in the circuit.

On the meter, the blackplug goes to COM, thered plug goes to mA or Aand the dial must be set to mA or A scale.

Measuring Voltage (V)

To measure V (also knownas “voltage drop”) across a circuit load, the meter has to be connected in parallelwith the load.

On the meter, the blackplug goes to COM, thered plug goes to V and the dial must be set to DC voltsscale (if using a battery circuit).