Circuits

• Electric Circuit: a closed path along which charged particles move

• Electric Current: the rate at which a charge passes a given point in a circuit.

• For current to flow the circuit must be complete and there must be a potential difference between two points in the circuit.

• The unit of current is the ampere (also known as an amp)

• Conductor: a material, usually a metal, in which electric charges move easily. There are plenty of free electrons.

• Insulators have few or no free electrons.

• Current can be described in two ways: conventional current and electron flow

• Conventional current: current flows from the positive to negative, against the flow of electrons

• Electron flow: current flows from negative to positive, a flow of electrons

• I = q/t where I = Current (amps), q = charge (Coulomb), and t = time (seconds)

• Example: During a thunderstorm, a lightning strike transfers 12 coulombs of charge in 2.0 x 10-3 second. What is the average current produced in this strike?

• Example: Charge flowing at the rate of 2.50 x 1016 elementary charges per second is equivalent to a current of ?

Some Circuit Components

• Switch: a device for making, breaking, or changing the connections in an electric circuit. The switch must be closed and there must be a complete circuit for current to flow.

• Light Bulb:

• Cell: a device that converts chemical energy to electrical energy.

• Battery: a combination of two or more cells.

• Batteries and cells can provide the potential difference needed for current to flow.

• Ammeter: a device used to measure current (Placed in the circuit)

• Voltmeter: a device used to measure the potential difference between two points (Placed over the circuit)

• Resistance: the opposition that a device or a conductor offers to the flow of electric current.

• Unit is the ohm (Ω)

• resistor : a device designed to impede the flow of current

• Used to represent an appliance like a toaster or hairdryer in a circuit

• Ohm’s law: for a constant temperature, the resistance of a conductor is the ratio of the potential difference applied to its ends and the current that flows through it.

• R = V/I where R = resistance (Ohm), V = potential difference (Volt), I = current (Amp)

• Example: A student measures a current of 0.10 ampere flowing through a lamp connected by short wires to a 12.0V source. What is the resistance to the lamp?

• Example: An automobile headlight with a resistance of 30 ohms is placed across a 12-V battery. What is the current through the circuit?

• Example: A motor with an operating resistance of 32 ohms is connected to a voltage source. The current in the circuit is 3.8 A. What is the voltage of the source?

• Example: A 20 ohm resistor has 40 C of charge passing through it in 5.0 seconds. What is the potential difference across the resistor?

• Electrical power: the rate at which electrical energy is transferred by an electrical circuit

• P = VI where P = power (watt), V = potential difference (volt),

I = current (amps)

• Given P = VI and V = IR we can also say that P = I2R

• Given P = VI and I = V/R we can also that that P = V2/R

• kilowatt hour: equal to 1000 watts delivered continuously for 3600 seconds (one hour) or 3.6x106 J

• Electrical Energy/Work: The power consumed during a specific amount of time

• W = Pt = VIt = I2Rt = V2t/R where W = energy/work (joules), P = power (watts), t = time (seconds)

• Given W = Pt and P = VI we can also say that W = VIt

• Given W = Pt and P = I2R we can also say that W = I2Rt

• Given W = Pt and P = V2/R we can also say that W = V2t/R

• Example: A television set draws 2.0 A when operated on 120V.

a.) How much power does the set use?b.) If the set is operated for an average of 7.0 hours per day, what energy is

kWh does it consume per month?c.) At $0.08 per kWh, what is the cost of operating the set per month?

• Example: A 60W light bulb is connected to an 115V power source.

a.) What is the current through the light bulb?b.) What is the resistance of the light

bulb?

• Example: A 240V water heater has a resistance of 15 ohms.

a.) What is the power of the heater? b.) What thermal energy is supplied by the heater in 15 minutes?c.) Compare the power of the same

240V water heater to a 120V water heater, also with a resistance of 15ohms.

d.) Compare the thermal energy of the 240V water heater to a 120V heater in a 15 minute period.

• Resistivity: a characteristic of a material that depends on its electronic structure and temperature (ρ)

• unit is the ohmmeter

• Resistance varies directly with length

• Resistance varies inversely with its cross-sectional area (Area of a wire is π r2 )

• Resistance varies directly with resistivity

• Good conductors have low resistivities.

• As temperature increases, resistivity increases

• R = ρL/A, where ρ= resistivity (ohmmeter), L = length (m), A = cross sectional area (m2), R = resistance (ohm)

• Cross sectional area, A = πr2

• Example: A 10.0 meter length of copper wire is at 20°C. The radius of the wire is 1.0x10-3 meter.

• a.) Determine the cross-sectional area of the wire.

• b.) Calculate the resistance of the wire.

• Example: A 10.0 meter long wire has a cross sectional area of 3.0x10-6m2 and a resistance of 9.4x10-2 ohm at 20°C. What material could this wire be made of?

• Example: A 12.0-meter length of copper wire has a resistance of 1.50 ohms. How long must an aluminum wire with the same cross-sectional area be to have the same resistance?