II. Electric current 1. Definition Units: [ I ] = 1A = 1 C/s Conventional current Electron flow Example: electrons passed through the electric conductor during 4 seconds. Find the electric current through this conductor. Example: The electric current of 0.5 A is flowing through the electric conductor. a) What electric charge is passing through the conductor during each second? b) What electric charge will pass through the conductor during 1 minute? a) b) 1

3. Resistance I V I V Nonohmic device 2. Ohm’s Law Definition:Units: [ R ] = 1Ω = 1 V/AOhm’s Law: 2

4. Resistivity L A I Resistivity: Example: What is the resistance of 1 m of nichrome wire of 2 mm diameter? 3

R1R1 R2R2 V1V1 V2V2 V Two resistors R 1 and R 2 are in series when they are connected one after the other 5a. Resistors in series IR eq V I 4

Two resistors R 1 and R 2 are in parallel when they are connected to the same potential difference 5b. Resistors in parallel R1R1 I1I1 R2R2 I2I2 II R eq V I 5

Example: A 2 A current flows into a series combination of a 3 Ω and a 4 Ω resistors. What is the voltage drop across the 4 Ω resistor? Example: A 3 A current flows into a parallel combination of 4 Ω, 6 Ω, and 12 Ω resistors. What current flows through the 12 Ω resistor? 6

Symbols for circuit elements Conductor (wire) with negligible resistance Resistors Battery Voltmeter (should be connected in parallel) Ammeter (should be connected in series) - + Switch Ground 7

A 6a. Ammeter (used to measure current) V A B 6b. Voltmeter (used to measure voltage or potential difference) Ammeter should be connected in series Ammeter has very small (ideally zero) internal resistance, so it does not affect the current to be measured Voltmeter should be connected in parallel Voltmeter has very large (ideally infinite) internal resistance, so that very little current is diverted through it. 8

6c. Voltmeter and Ammeter Example: What connection is not correct? B C A Voltmeter should be connected in parallel Ammeter should be connected in series Voltmeter has very large (ideally infinite) internal resistance Ammeter has very small (ideally zero) internal resistance 9

7. Power in electric circuits R V I 10

Example: Two resistors, R 1 = 5 , R 2 = 10 , are connected in series. The battery has voltage of V = 12 V. a) Find the electric power delivered by the battery b) Find the electric power dissipated in each resistor + Power in the resistor R 1 : Power in the resistor R 2 : The total power: 11

Example: Two resistors, R 1 = 5 , R 2 = 10 , are connected in parallel. The battery has voltage of V = 12 V. a) Find the electric power delivered by the battery b) Find the electric power dissipated in each resistor Power in the resistor R 1 : Power in the resistor R 2 : The total power: + Power delivered by battery: 12

Example: How much energy does a typical appliance use? Let’s look at 1000 W hair dryer. We use it for 10 minutes, electricity costs ~10 cents per kW  h. How much did running the hair dryer cost? What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time (E = Pt). We have been measuring energy in joules, but the electric company measures it in kilowatt-hours (kWh). 1 kWh = 1000 J/s x s = J 7a. Kilowatt-hours (kWh) 13

8. Alternating current I0I0 -I 0 t DC current t AC current T Example: V0V0 -V 0 t t T I0I0 - current amplitude V0V0 - voltage amplitude T – period f - frequency It is common to describe AC current and AC voltage with, so called, root mean square (RMS) values: 14

8a. RMS – what it is? (Optional) 15