Ch 181 Chapter 18 Electric Currents

Ch 182 Simple Electric Cell Sulfuric acid Zn ______ Carbon Electrode (+) Zn Electrode (-) Two dissimilar metals or carbon rods in acid Zn + ions enter acid leaving terminal negative Electrons leave carbon making it positive Terminals connected to external circuit ‘Battery’ referred to several cells originally

Ch 183 Electric Current If we connect a wire between the two terminals electrons will flow out of the negative terminal and toward the positive terminal  we have an electric current. Electric current I is defined as the net amount of charge that flows past a given point per unit time. 1 C/s = 1A (ampere) An ampere is a large current and often currents are mA (10 -3 A) or  A (10 -6 A).

Ch 184 Electric Circuit It is necessary to have a complete circuit in order for current to flow. The symbol for a battery in a circuit diagram is: + _ Device +

Ch 185 “Conventional” current direction is opposite to actual electron flow direction which is – to +.

Ch 186 Ohm’s Law For wires and other circuit devices, the current is proportional to the voltage applied to its ends: I  V The current also depends on the amount of resistance that the wire offers to the electrons for a given voltage V. We define a quantity called resistance R such that V = I R (Ohm’s Law) The unit of resistance is the ohm which is represented by the Greek capital omega (  ). Thus

Ch 187 Resistors A resistor is a circuit device that has a fixed resistance. Resistor Circuit symbol Resistors obey Ohm’s law but not all circuit devices do (semi- conductor diode, LED) I V0 I V0 Resistor non-ohmic device

Ch 188 Example: A person experiences a mild shock if a current of 80  A flows along a path between the thumb and the index finger. The resistance of this path is 4.0x10 5  when the skin is dry and 2000  when the skin is wet. Calculate the minimum voltage difference between these two points that will produce a mild shock.

Ch 189 Example: A person experiences a mild shock if a current of 80  A flows along a path between the thumb and the index finger. The resistance of this path is 4.0x10 5  when the skin is dry and 2000  when the skin is wet. Calculate the minimum voltage difference between these two points that will produce a mild shock.

Ch 1810 Example: Calculate the number of electrons per second that flow past a point on the skin in the previous example.

Ch 1811 Example: Calculate the number of electrons per second that flow past a point on the skin in the previous example.

Ch 1812 Power in Electric Circuits Electrical circuits can transmit and consume energy. When a charge Q moves through a potential difference V, the energy transferred is QV. Power is energy/time and thus: and thus:

Ch 1813 Notes on Power The formula for power applies to devices that provide power such as a battery as well as to devices that consume or dissipate power such as resistors, light bulbs and electric motors. For ohmic devices, the formula for power can be combined with Ohm’s Law to give other versions:

Ch 1814 Household Power Electric companies usually bill by the kilowatt-hour (kWh.) which is the energy consumed by using 1.0 kW for one hour. Thus a 100 W light bulb could burn for 10 hours and consume 1.0 kWh. Electric circuits in a building are protected by a fuse or circuit breaker which shuts down the electricity in the circuit if the current exceeds a certain value. This prevents the wires from heating up when carrying too much current.

Ch 1815 Connection of Household Appliances

Ch 1816 Example: A person turns on a 1500 W electric heater, a 100 W hair dryer and then a 300 W stereo. All of these devices are connected to a single 120 V household circuit that is connected to a 20 A circuit breaker. At what point will the circuit breaker trip off?

Ch 1817 Example: A person turns on a 1500 W electric heater, a 100 W hair dryer and then a 300 W stereo. All of these devices are connected to a single 120 V household circuit that is connected to a 20 A circuit breaker. At what point will the circuit breaker trip off?

Ch 1818 Example: If electricity costs $ per kWh in Nova Scotia, calculate the cost of operating all the appliances in the previous problem for 2.0 hours.

Ch 1819 Example: If electricity costs $ per kWh in Nova Scotia, calculate the cost of operating all the appliances in the previous problem for 2.0 hours.

Ch 1820 Microscopic View of Current Read Example on page 545. It studies a 5.0A current in a copper wire that is 3.2 mm in diameter. It finds that the average “free” electron moves with a velocity of 4.7 x m/s in the direction of the current. This is called the drift velocity. It also assumes the “free” electrons behave like an ideal gas and calculates that the thermal velocity of the average electron is 1.2 x 10 5 m/s. Thus in a wire carrying a current, the electron motion is largely random with a slight tendency to move in the direction of the current. Thus if you could see electrons in a wire carrying current they would appear to be moving randomly.

Ch 1821 Summary of Units

Ch 1922 Chapter 19 DC Circuits

Ch 1923 EMF Devices that supply energy to an electric circuit are referred to as a source of electromotive force. Since this name is misleading, we just refer to them as source of emf (symbolized by  and a slightly different symbol in the book.) Sources of emf such as batteries often have resistance which is referred to as internal resistance.

Ch 1924 Terminal Voltage r  ab V ab We can treat a battery as a source of  in series with an internal resistor r. When there is no current then the terminal voltage is V ab =  But with current I we have: The internal resistance is small but increases with age.

Ch 1925 Circuit Symbols

Ch 1926 Resistors in Series - Derivation We want to find the single resistance R eq that has the same effect as the three resistors R 1, R 2, and R 3. Note that the current I is the same throughout the circuit since charge can’t accumulate anywhere. V is the voltage across the battery and also V = V 1 + V 2 + V 3 Since V 1 = I R 1 etc., we can say The equivalent equation is V=IR eq and thus

Ch 1927 Summary - Resistors in Series The current I is the same throughout the circuit since charge can’t accumulate anywhere.

Ch 1928 Resistors in Parallel - Derivation This is called a parallel circuit Notice V 1 = V 2 = V 3 = V Since charge can’t disappear, we can say We can combine these equations with V = IR eq to give

Ch 1929 Summary - Resistors in Parallel The electric potential (voltage) is the same across each resistor V 1 = V 2 = V 3 The current through the battery splits several ways I = I 1 + I 2 + I 3 Can be 2, 3 or more resistors in parallel.

Ch 1930 Example: A 3.0 V battery is connected to three resistors as shown. Calculate the resistance of the equivalent circuit and the power dissipated in the equivalent circuit. R 1 = 500 Ω, R 2 = 1000 Ω and R 3 = 2000 Ω.

Ch 1931 Example: A 3.0 V battery is connected to three resistors as shown. Calculate the resistance of the equivalent circuit and the power dissipated in the equivalent circuit. R 1 = 500 Ω, R 2 = 1000 Ω and R 3 = 2000 Ω.

Ch 1932 Example: From the previous example, calculate the current and the power dissipated in each resistor and the total power dissipated in the circuit.

Ch 1933 Example: From the previous example, calculate the current and the power dissipated in each resistor and the total power dissipated in the circuit.

Ch 1934 Example: A 3.0 V battery is connected to 4 resistors as shown. Calculate the resistance of the equivalent circuit and the current in the equivalent circuit. R1 = 500 Ω, R2 = 1000 Ω, R3 = 1000 Ω, and R4 = 2000 Ω.

Ch 1935 Example: A 3.0 V battery is connected to 4 resistors as shown. Calculate the resistance of the equivalent circuit and the current in the equivalent circuit. R1 = 500 Ω, R2 = 1000 Ω, R3 = 1000 Ω, and R4 = 2000 Ω.

Ch 1936 Ammeter To measure current ammeter must be connected in series. Must have small internal resistance or it will reduce current and give a faulty measurement.

Ch 1937 Voltmeters To measure voltage difference, it must be connected in parallel. Must have high internal resistance or it will draw too much current which reduces voltage difference and gives a faulty measurement.