chapter 6: electric...

Chapter 6: Electric Circuits

Electric Circuits

• Electrons possess electric potential energy that can be transformed into heat, light, and motion.

• For such transformations to occur, a source of electric potential energy needs to connect to one or more components by means of an electric circuit (path for electric current)

• Any device in a circuit that converts electric potential energy into some other form of energy (causing an electric potential drop) is called a resistor

• In the adjacent circuit, the charges pass from the positiveterminal of the battery, through the light bulb, and then back to the negative terminal of the battery.

• Electric potential energy acquired in the battery is carried by electric charges as they pass through the circuit.

• The electric potential energy is transferred to the light bulb and converted to light and heat.

• Electric current can only flow through a circuit if there is a continuous conducting path.

• Any break in the circuit will stop the flow.

Circuits

• Any circuit can be represented with a schematic diagram using a set of common symbols:

Series Circuits

• Simple way of joining several loads together

• Charges have only oneconducting path

Parallel Circuits

• Charges can move along several paths through the circuit

• Charge could pass through only one of the several loadsbefore returning to the energy source.

Cells vs. Batteries

• Chemical Cell – electrochemical device that converts chemical energy into electrical energy

• Battery – collection of cells that work together to provide electrical energy to a circuit

Cells in Series

• Positive terminal is connected to negative terminal of another cell

• Voltage is cumulative

Cells in Parallel

• Positive terminals are connected together

• Voltage is constant, but increases the current that flows

Resistance

• When charges pass through a material or device, they experience a resistance to their flow

• This results in a loss of electrical potential energy

Ohm’s Law

• German scientist Georg Ohm (1787-1854) found that, for any conductor, the ratio of voltage to current is constant

• The potential difference between any two points in a conductor varies directly as the current between the two points (if the temperature remains constant).

R = V/I

R = resistance (ohms - )

V = potential difference (volts - V);

I = current (amperes - A)

Ex.1: What is the resistance in a toaster, connected to a 120V power supply, if the current through it is 8.7 A?

Ex.2: Calculate the maximum rating (in volts) of a battery used to operate a toy electric motor that has a resistance of 2.4 and runs at top speed with a current of 2.5 A.

Ex.3: How much current is supplied by a 6 V battery if it is connected to a light bulb with a resistance of 20 ?

Power in Electric Circuits (Joule’s Law)

• To predict the amount of energy used by an electrical device, we first need to know the amount of time the device will be used.

E = VIt

P = E/t

Therefore, P = VIt/t or P = VI

Since P = VI and V = IR Since P=VI and I = V/R

Then P = (IR) I Then P = V (V/R)

P = I2R P = V2/R

Ex.1: Calculate the resistance of a 7.5 W light bulb plugged into a 120 V household outlet.

Ex.2: What is the power rating on a light bulb with a resistance of 240 if a 0.50A current runs through it?

Ex.3: A 110 V household circuit contains a 1800 W microwave and an 800 W coffee maker, which are connected to a 20 A fuse. Will the fuse melt if both the microwave and coffeemaker are on?

Kirchhoff’s Laws for Electric Currents

Law of Conservation of Energy

• As electrons move through an electric circuit, they gain energy in sources and lose energy in loads

• The total energy gained in one trip through a circuit is equal to the total energy lost.

Law of Conservation of Charge

• Electric charge is neither created nor lost in an electric circuit, nor does it accumulate at any point in the circuit.

Kirchhoff’s Voltage Law

• Around any complete path through an electric circuit, the sum of the increases in electric potential is equal to the sum of the decreases in electric potential

Kirchhoff’s Current Law:

• At any junction point in an electric circuit, the total electric current into the junction is equal to the total electric current out.

Resistance

Remember…

• When charges pass through a material or device, they experience a resistance to their flow

Resistance in Series

Vs = V1 + V2 + V3

IsRs = I1R1 + I2R2 + I3R3

Since Is = I1 = I2 = I3

Then Rs = R1 + R2 + R3

• Equivalent Resistor: Resistor that has the same current and potential difference as the resistors it replaces.

Ex.1: What is the equivalent resistor in a series circuit containing a 16 light bulb, a 27 heater, and a 12 motor?

Ex.2: A 22 , and 18 and an unknown resistor are connected in series to give an equivalent resistance of 64 . What is the resistance of the unknown resistor?

Resistance in Parallel

IP = I1 + I2 + I3

I1 = V1/R1 I2 = V2/R2 I3 = V3/R3

VP/RP = V1/R1 + V2/R2 + V3/R3

Since VP = V1 = V2 = V3

1/RP = 1/R1 + 1/R2 + 1/R3

Example #1: Find the equivalent resistor when a 4.0 bulb and a 8.0 bulb are connected in parallel.

Example #2: Calculate the equivalent resistance of two, three, four and five 60 bulbs in parallel. What is the simple relationship for the equivalent resistance of in equal resistances in parallel?

1. 2.

3. 4.

Resolve the following circuits:

CircuitPosition

Voltage (V)

Current (A)

Resistance(ohms)

1 10.0

2 20.0

3 30.0

Total 6.0

Resolve the following circuits:

CircuitPosition

Voltage (V)

Current (A)

Resistance(ohms)

1 10.0

2 20.0

3 30.0

Total 6.0

Resolve the following circuits: CircuitPosition

Voltage (V)

Current (A)

Resistance

(ohms)

1 10.0

2 20.0

3 30.0

Total 6.0

Resolve the following circuits: CircuitPosition

Voltage (V)

Current (A)

Resistance

(ohms)

1 80.0

2 20.0

3 20.0

4 30.0

Total 120