Circuits!

What’s a Circuit? A circuit is a closed path where positive charges flow from high to low potential energy. They can be manipulated on the way.

The Power Source Provides the difference in potential (potential energy per unit charge). It is measured in volts (remember this) A Cell (battery) is the easiest to see. It converts chemical energy to electrical energy. This is also called “Electromotive force” (or emf) Think of “Voltage” as “pressure” that causes charges to move.

What is Electric Current? An electric current is the flow of electrons through wires and components. The greater the current, the more charges are moving! In which direction does the electrons flow? It flows from the negative terminal to the positive terminal. Measured in Amperes (we say Amps) - +

Conventional Current + - Electron flow: The direction of e- flowing from – to +. Electron flow + - e- Conventional current: The motion of +q from + to – has same effect. Conventional flow + Electric fields and potential are defined in terms of +q, so we will assume conventional current (even if electron flow may be the actual flow).

Electric Current Electric current I is the rate of the flow of charge Q through a cross-section A in a unit of time t. A + - Wire +Q t One ampere A is charge flowing at the rate of one coulomb per second.

Resistance When an object (like a light bulb) resists or diminishes the flow of current, it has resistance. Resistance is measured in Ohms Symbol for Ohms: Ω

Factors Affecting Resistance 1. The length L of the material. Longer materials have greater resistance. 1 W L 2 W 2L 2. The cross-sectional area A of the material. Larger areas offer LESS resistance. 1 W 2A 2 W A

Factors Affecting R (Cont.) 3. The temperature T of the material. The higher temperatures usually result in higher resistances. R > Ro Ro 4. The kind of material. Iron has more electrical resistance than a geometrically similar copper conductor. Ri > Rc Copper Iron

Resistivity of a Material The resistivity r is a property of a material that determines its electrical resistance R. Recalling that R is directly proportional to length L and inversely proportional to area A, we may write: The unit of resistivity is the ohm-meter (W·m)

Water Analogy to EMF Low pressure Pump Water High pressure Valve Water Flow Constriction Source of EMF Resistor High potential Low potential Switch R I + - The source of emf (pump) provides the voltage (pressure) to force electrons (water) through electric resistance (narrow constriction).

Ohm’s Law Relates the voltage (Volts), current (Amps), and resistance (Ohms) in a circuit. V = Voltage (in Volts) I = Current (in Amps) R = Resistance (in Ω)

Ohmic Resistors An ohmic resistor obeys Ohm’s law. A graph of voltage vs current gives a straight line with a positive slope. The steeper the slope, the higher the resistance will be.

Nonohmic Resistors A bulb is a nonohmic resistor. Its voltage-current graph does not follow a straight line. Instead, it gives a curve with an increasing slope. It shows that the resistance increases as the current increases.

Power Power describes the rate at which electrical energy is transferred. It is measured in Watts (W). P = Power (Watts) I = Current (Amps) V = Voltage (Volts) OR..

A light bulb has a resistance of 30Ω A light bulb has a resistance of 30Ω. What voltage would be required to run 4 Amperes of current through the bulb? 120 V 7.5 V .13 V Voltron [Default] [MC Any] [MC All]

A toaster is connected to a 120-Volt circuit and has 6 Amps of current running through it. What is the resistance of the toaster? 720 Ω 20 Ω .05 Ω Depends on how brave he is. [Default] [MC Any] [MC All]

If your body resistance is 100,000 Ω, how much current will you experience if you touch the terminals of a 12-Volt battery? 1,200,000 A 8,333 A .00012 A Depends on how good it taste [Default] [MC Any] [MC All]

How much power is dissipated in a toaster if it is connected to a 120-Volt circuit and uses 8 Amps? Zero, it is powered by imagination [Default] [MC Any] [MC All]

A light bulb has a power rating of 60-Watts A light bulb has a power rating of 60-Watts. How much current would it pull if it has a resistance of 15 Ohms? 4 A 2 A 900 A 30 A [Default] [MC Any] [MC All]

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Circuit Diagram We draw electric circuits using specific symbols (because quite frankly most people can’t draw)…. cell resistor switch wires

Types of Circuits There are two basic types of electrical circuits; SERIES CIRCUITS PARALLEL CIRCUITS

SERIES CIRCUITS The components are connected end-to-end, one after the other. They make a simple loop for the current to flow round. If one bulb ‘blows’ it breaks the whole circuit and all the bulbs go out. (One charge gets stuck, they all get stuck).

PARALLEL CIRCUITS The components are connected side by side. The current has a choice of routes. If one bulb ‘blows’ there will still be a complete circuit to the other bulb so it stays alight.

“Short Circuit” Just remember that electricity is lazy, and will always take the path of least resistance. If something (usually a wire) provides a path around a resistor, the electrons will take it!

COMPLEX CIRCUITS Is made up of both series and parallel circuits combined. This is what most circuits in the “real world” are like.

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Resistances in Series Resistors are said to be connected in series when there is a single path for the current. R1 I VT R2 R3 Only one current The current I is the same for each resistor R1, R2 and R3. The energy gained through E is lost through R1, R2 and R3. The same is true for voltages: For series connections: I = I1 = I2 = I3 VT = V1 + V2 + V3

Equivalent Resistance: Series The equivalent resistance Re of a number of resistors connected in series is equal to the sum of the individual resistances. VT = V1 + V2 + V3 ; (V = IR) R1 I VT R2 R3 Equivalent Resistance ITRe = I1R1+ I2R2 + I3R3 But . . . IT = I1 = I2 = I3 Re = R1 + R2 + R3

Summary: Single Loop Circuits: Resistance Rule: Re = SR Voltage Rule: SE = SIR

For Parallel Resistors: Parallel Connections Resistors are said to be connected in parallel when there is more than one path for current. For Parallel Resistors: Parallel Connection: 6 W 2 W 4 W V2 = V4 = V6 = VT I2 + I4 + I6 = IT For Series Resistors: 2 W 4 W 6 W Series Connection: I2 = I4 = I6 = IT V2 + V4 + V6 = VT

Equivalent Resistance: Parallel VT = V1 = V2 = V3 Parallel Connection: R3 R2 VT R1 IT = I1 + I2 + I3 Ohm’s law: The equivalent resistance for Parallel resistors:

Series and Parallel Combinations In complex circuits resistors are often connected in both series and parallel. VT R2 R3 R1 In such cases, it’s best to use rules for series and parallel resistances to reduce the circuit to a simple circuit containing one source of emf and one equivalent resistance. VT Re

Example 4. Find the equivalent resistance for the circuit drawn below (assume VT = 12 V). Re = 4 W + 2 W Re = 6 W 12 V 2 W 4 W 6 W 12 V

Example 3 (Cont.) Find the total current IT. Re = 6 W VT 3 W 6 W 4 W 12 V 2 W IT IT = 2.00 A

This can also be found from V3,6 = I3,6R3,6 = (2 A)(2 W) V3 = V6 = 4 V Example 3 (Cont.) Find the currents and the voltages across each resistor. I4 = IT = 2 A VT 3 W 6 W 4 W V4 = (2 A)(4 W) = 8 V The remainder of the voltage: (12 V – 8 V = 4 V) drops across EACH of the parallel resistors. This can also be found from V3,6 = I3,6R3,6 = (2 A)(2 W) V3 = V6 = 4 V (Continued . . .)

Example 3 (Cont.) Find the currents and voltages across each resistor. V4 = 8 V V6 = V3 = 4 V VT 3 W 6 W 4 W I3 = 1.33 A I6 = 0.667 A I4 = 2 A Note that the junction rule is satisfied: SI (enter) = SI (leaving) IT = I4 = I3 + I6

Kirchoff’s Laws for DC Circuits Kirchoff’s first law: The sum of the currents entering a junction is equal to the sum of the currents leaving that junction. Junction Rule: SI (enter) = SI (leaving) Kirchoff’s second law: The sum of the emf’s around any closed loop must equal the sum of the IR drops around that same loop. Voltage Rule: SE = SIR

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