Chapter 20 Circuits And Circuit Elements

20.1 Schematic Diagrams and Circuits Objectives 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

Schematic Diagram …is a graphic representation of an electric circuit, with standardized symbols representing circuit components (aka, circuit diagram)

Circuit Elements and Symbols

Draw the schematic for this circuit

Interpret the circuit elements in this schematic

Electric Circuit …a set of electrical components connected so that they provide one or more complete paths for the 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

A couple more definitions…. 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. 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 from the battery. The terminal voltage (Vt) is the actual maximum voltage available from the battery, which is Slightly less than emf due to the internal resistance (r) of the battery.

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

20.2 Resistors in Series or in Parallel Objectives 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 vs Parallel 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 Circuit Parallel Circuit

Calculations for Resistors in Series Resistors in series all have the same current running through them ΔVt = ΔV1 + ΔV2 + ΔV3…. and ΔV = IR but I is the same everywhere So, IReq = IR1 + IR2 + IR3… 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   It = I1 + I2 + I3…   But ΔV is the same everywhere, so…  

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 circuit Series circuits require all elements to conduct Parallel circuits do not require all elements to conduct

SERIES PARALLEL Req = 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 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 circuit b) 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 circuit b) What is Req? c) What is I?

Answers a) Req = 18.0 Ω b) I = 0.50 A 2. a) Req = 0.917 Ω b) I = 9.8 A

20.3 Complex Resistor Combinations Objectives Calculate the equivalent resistance for a complex circuit involving both series and parallel portions Calculate the current in and the potential difference across individual elements within a complex circuit

Combination of some resistors in series and some resistors in parallel 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

What is I at R4? What is ΔV across R4? 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 A ΔV across R4 = 22.5 V

Complex Circuit Example Req = ? It = ? c) V across 2.0 resistor = ? d) I in 4.0 resistor = ?

Solving Complex Circuits with Kirchoff’s Rules The sum of the currents entering any junction must equal the sum of the currents leaving that junction. 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 junction 2. 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 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 Choose a loop direction 2. If you cross the battery from negative to positive then you gain energy so ADD ΔV 3. If you cross the battery from positive to negative then you lose energy so SUBTRACT ΔV 4. If your loop direction is the same as the current direction as you cross a resistor then SUBTRACT IR 5. If your loop direction is opposite the current direction 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 through the 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, the current must flow through the meter, therefore the meter has to be connected in series in the circuit. On the meter, the black plug goes to COM, the red plug goes to mA or A and the dial must be set to mA or A scale.

Measuring Voltage (V) To measure V (also known as “voltage drop”) across a circuit load, the meter has to be connected in parallel with the load. On the meter, the black plug goes to COM, the red plug goes to V and the dial must be set to DC volts scale (if using a battery circuit).