© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED Basic DC Circuits Review

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDPrefixes PrefixesSymbolValue attoa femtof picop nanon10 -9 microµ10 -6 millim10 -3 kilok10 3 megaM10 6 gigaG10 9 teraT10 12 Prefixes come in handy when trying to express high or low numbers. EXAMPLES: 1,000 1 k 5.68× m µ 1,212,000, G p 2.5× p

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED Voltage (V) Voltage is an electrical pressure which causes current to flow through a resistance. (Batteries) Two common DC voltage supplies are shown below: The “long side” or + terminal of a battery is called the anode. It is measured in volts (V). The “short side” or – terminal of a battery is called the cathode.

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDVoltage Voltage can be compared to the pressure of water in a tank. As the height of water in a tank increases, so does the water pressure. This increase in pressure causes more water to flow out of an opening in the bottom of a tank, much like how a higher voltage (higher electrical pressure) produces more current through a resistance. Continued… 9 V 3 Ω 3 A 6 V 2 A 3 V 1 A

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED Here we get V, since the red lead is hooked to the negative terminal of the battery and the black is connected to the positive terminal. Voltage Polarity Voltage polarity is denoted by a + and – symbol. When connecting the positive (red) lead of a multimeter to the positive terminal of the battery with the negative (black) lead to the negative terminal of the battery, a positive value of voltage will be displayed. However, if you were to connect the red lead to the negative terminal and the black lead to the positive terminal, a negative voltage would be displayed. Let’s look at the following source: 9.15 V Digital Multimeter V Now let’s see what happens when polarity is reversed V + - VoVo V o = 9.15 V - + V o = V Here we get 9.15 V, since the red lead is hooked to the positive terminal of the battery and the black is connected to the negative terminal. The multimeter is essentially an open circuit when measuring voltage.

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED Current (I) Current is the movement of electrons through a conductor. It is established by a potential difference (or voltage) across a resistance and is measured in the quantity amperes or amps (A). The common DC current source is shown below: (Independent Current Sources) The arrow of the independent current source represents the direction of current flow.

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDCurrent Current is not across two points as is voltage, but flows through a circuit element. Let’s consider the following circuit: Digital Multimeter mA 1 kΩ 9 mA 1 kΩ 9 mA Click to see what happens when leads are switched. -9 mA Note: Multimeter is set to measure current here. It essentially acts as a short circuit to take this measurement. I I Current is denoted positive when entering the red (positive) lead. Current is denoted negative when entering the black (negative) lead.

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDCurrent Current can only flow through a closed loop. It must travel where there is a defined path. This concept is pictured below with current depicted in red. Notice, there is zero current flow through R 3, since there is no closed path for current to flow. R1R1 R3R3 R2R2 Continued…

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDNodes A node is a connection between one or more elements in a circuit. Here, the nodes of each circuit are circled in red. Notice that the wires composing each node have no resistance, thus there is no voltage drop within the red areas. Note: When taking measurements with a digital multimeter the negative lead is connected to ground (node 1).

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDNodesContinued… Digital Multimeter + - Next, we will use the digital multimeter to measure node voltages in a circuit containing two nodes. 9 V R1R1 R2R2 R3R3 R4R4 R5R5 Notice that this voltage reading is also 9 V and that the voltage dropped across R 2 is equal to the voltage across R 1. The reason is because both of these resistors share the same two nodes. The voltage across R 3 and R 4 (taken at the outer nodes) is also 9 V because these are the same two nodes as those shared across R 2 and R 1. From the previous slides, you might have known that this configuration would result in a read out of 9 V. However, you might not have known that the voltage dropped across R1 was also 9 V. For the same reason we also measure the same 9 V across R 5.

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDNodesContinued… Digital Multimeter V R1R1 R2R2 R3R3 R4R4 R5R5 Now we are going to take a closer look at the previous example to see the effects of choosing a reference point when measuring node voltage. Previously, when measuring the voltage across R 3 and R 4, we determined the voltage to be 9 V. This is because we are measuring the top (red) node in reference to ground (the purple node). 9 V What result would we get when measuring the top (red) node in reference to the orange node located between R 3 and R 4 ? ??? The measurement would be a value of voltage less than 9 V but greater than 0 V. < 9 V Now, Can you guess what the multimeter would read when measuring the voltage of the top (red) node with respect to itself? 0 V If your answer was 0 V, then you were correct!

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDBranches A branch is a part of a circuit that contains one or more circuit elements in series with a separate node at each end. Notice that, the current flowing through a branch is equal for every element contained in the branch network. For example, V R1R1 R2R2 R3R3 R4R4 R5R5 R6R6 ISIS I1I1 I2I2 I3I3 Note: The current I 1 flows through R 1, R 2, and R 3. The value of I 1 does not change through the branch.

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED Resistance (R) Resistance is a hindrance/opposition to the passage of an electrical current. Resistance in a circuit is represented by a resistor. The unit of resistance is the ohm (Ω). The symbol used to represent a resistor is schematic captureactual representation Materials such as metal (conductors) have a small resistance, where materials such as rubber (insulators) have a large resistance.

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED Capacitance (C) Capacitance is the ratio of charge to voltage across two conductive elements (or plates). Capacitance is represented by a capacitor in circuits and measured in farads (F). A farad is a very large value of capacitance. A more likely value of capacitance would be 0.01 µF (1x10 -8 F). The symbol used to represent a capacitor is schematic capture actual representation Some capacitors, especially electrolytic capacitors, are polarized. + -

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED Capacitance Continued When analyzing a steady-state DC circuit, capacitors act as open circuits—meaning there is no steady-state DC current flowing through them (infinite resistance). Continued… C V R1R1 R2R2 C R3R3 V R1R1 R2R2 R3R3 R = ∞ Ω

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDInductance When analyzing a steady-state DC circuit, inductors act as short circuits— meaning that steady-state current is passed directly through them (zero resistance). Continued… V R1R1 R2R2 L R3R3 V R1R1 R2R2 R3R3 R = 0 Ω L

© 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED Material Properties Resistivity (ρ)– Resistivity is the intrinsic property that accounts for the nature of a material. It is defined as the ability of a material to resist electrical conduction, with units ohm-meter (Ωm). The resistance of a material is related to its resistivity such that: R = ρ (L/A) where, ρ = resistivity of material L = length of conductor which current flows along A = cross-sectional area of conductor that current flows through w h L Some Material I

Increasing the length of the resistor increases the resistance Increasing the cross sectional area of the resistor decreases the resistance © 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED

Material Properties Conductivity (σ) – Conductivity is the inverse of resistivity. It is defined as the ability of a material to conduct electricity, with units inversed ohm-meter (Ωm -1 ). Continued… σ = conductivity of material L = length of conductor which current flows through A = cross-sectional area of conductor that current flows through G = σ (A/L) = 1/R, where The conductance of a material is related to its conductivity by: w h L Some Material I

Increasing the cross sectional area of the conductor increases the conductance Increasing the length of a conductor decreases the conductance © 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVED

Ohm’s Law V = Voltage (Volts = V) I = Current (Amperes = A) R = Resistance (Ohms = Ω)

Ohm’s Law continued The total resistance of a circuit is dependant on the number of resistors in the circuit and their configuration Series Circuit Parallel Circuit

Kirchhoff’s Current Law Current into junction = Current leaving junction The amount of current that enters a junction is equivalent to the amount of current that leaves the junction

Kirchhoff’s Voltage Law Net Voltage for a circuit = 0 Sum of all voltage rises and voltage drops in a circuit (a closed loop) equals zero

Series Circuit Current is constant Why? –Only one path for the current to take

Parallel Circuit Voltage is constant Why ? –There are 3 closed loops in the circuit

The Light Bulb and its Components Has two metal contacts at the base which connect to the ends of an electrical circuit The metal contacts are attached to two stiff wires, which are attached to a thin metal filament. The filament is in the middle of the bulb, held up by a glass mount. The wires and the filament are housed in a glass bulb, which is filled with an inert gas, such as argon.

Light bulbs and Power Power dissipated by a bulb relates to the brightness of the bulb. The higher the power, the brighter the bulb. Power is measured in Watts [W] For example, think of the bulbs you use at home. The 100W bulbs are brighter than the 50W bulbs.

Bulbs in series experiment One bulb connected to the batteries. Add another bulb to the circuit in series. Q: When the second bulb is added, will the bulbs become brighter, dimmer, or not change? We can use Ohm’s Law to approximate what will happen in the circuit in theory:

Bulbs in series experiment continued…

Bulbs in parallel experiment One bulb connected to the batteries. Add a second bulb to the circuit in parallel. Q: What happens when the second bulb is added?  We can use Ohm’s Law to approximate what will happen in the circuit:

Bulbs in parallel experiment continued…

How to use a voltmeter: Voltmeter: - connect either end of the meter to each side of the resistor If you are reading a negative value, you have the probes switched. There should be no continuity beeping. If you hear beeping, STOP what you are doing and ask someone for help!

Voltmeter

Voltage: Probes connect to either side of the resistor Measuring Voltage

Breadboards You encountered breadboards early in the year. Let’s review them: The breadboard How the holes on the top of the board are connected:

Series Resistors are connected such that the current can only take one path

Parallel Resistors are connected such that the current can take multiple paths