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Ohm’s Law Physics Dr. Robert MacKay Voltage (Volts) Electrical Pressure - + + - V Current (Amps) Charge Flow I + + + V - + + + + + + + + Resistance, R (Ohms, Ω) Impedence I - - - V - - + - - - - - R Depends on Temperature Material of wire Area of wire Length of wire - Resistance, R (Ohms, Ω) Impedence Area - - - - - - - - Length R Depends on: * Temperature * Material of wire * Cros sectional Area * Length - - Resistance and Resistivity L R A = resistivity R=resistance Material Silver Copper Carbon Silicon Glass Rubber (ž- m) -8 1.59x10 -8 1.70x10 -5 3.6x10 2 2.5x10 12 10 15 10 (°C-1) -3 6.1x10 -3 6.8x10 -4 -5.0x10 -2 -7.0x10 1 0T R R0 T R R 0 (1 T) 0 (1 T) As a wire heats it up its resistance increases. Some thermometers work on this principle. Ohm’s Law V= I R I - - - V - - + - - - - - - Exercise Find the electric voltage required to have 10 Amps of current flow through a 2 Ω resistor. Given: I= 10 A and R=2 Ω Wanted: V Solution: V=I R V= (10 A) (2 Ω) = 20 Volts Exercise Find the electric current flowing in a 10 Ω resistor (light bulb) when connected to a 20 Volt battery. Given: V= 20 Vand R=10 Ω Wanted: I Solution: I= V=I R or I=V / R (20 V) / (10 Ω) = 2 Amps Exercise When a 60 Volt battery is connected to a circuit 4.0 amps of current flow from the battery. What is the circuit’s resistance. Given: V= 60 V and I=4.0 Amps Wanted: R Solution: I= V=I R or R=V / I (60 V) / (4.0 Amps) = 15 Ω Electric Power (Watts) Power = Current x Voltage 1 Watt = Amp x Volt Curcuits R=10 Ω R 10 Ω I P= ? I =? A V P V= 20 V 20 V V= I R or I=V/R Curcuits R=10 Ω P= ? R 10 Ω I 2.0 A V 20 V I =? A P V= 20 V V= I R or I=V/R Curcuits R=10 Ω P= ? R 10 Ω I 2.0 Amps V 20 V P 40.0 Watts I =? A V= 20 V P= I V = 2A(20V) = 40W Curcuits R=? R I P= 60 W I =? A V= 120 V V 120 V P 60 W Curcuits V= I R R=? R I P= 60 W I =? A V 120 V P 60 W V= 120 V P= I V or I=P/V=60W/120V=0.5A Curcuits R=? R P= 60 W I 0.50A V 120 V P 60 W I =? A V= 120 V Curcuits R=? R P= 60 W I 0.50A V 120 V P 60 W I =? A V= 120 V R=V/I=120V/0.5A=240W Curcuits R=? P= 60 W R 240W I 0.50A V 120 V P 60 W I =? A V= 120 V Curcuits R=10 Ω I =2 A P= 40 Watts A V= 20 V R 10 Ω I 2A V 20 V P 40 Watts Two light bulbs are connected in series to a battery the resistance of each is 20 W. What is the total effective resistance of this series combination? Two light bulbs are connected in series to a battery the resistance of each is 20 W. What is the total effective resistance of this series combination? Req=R1+R2= 20 W20 W40 W Two light bulbs are connected in series to a 40 Volt battery. The resistance of each is 20 W. What is the total Current leaving the battery? Two light bulbs are connected in series to a 40 Volt battery. The resistance of each is 20 W. What is the total Current leaving the battery? V=I R or I=V/R (R=Req=40 W) I=40V/40 W =1.0 Amp Curcuits R=10 Ω I =2 A P= 40 Watts A V= 20 V R 10 Ω I 2A V 20 V P 40 Watts A bit of trivia When 2 equal resistors are connected in parallel the effective resistance is half the value of each. (two 10 W resistor Req=5 W) When 3 equal resistors are connected in parallel the effective resistance is one-third the value of each. (three10 W resistor Req=3.33 W) When 4 equal resistors are connected in parallel the effective resistance is one-forth the value of each. (four10 W resistor Req=2.5 W) When N equal resistors are connected in parallel the effective resistance is 1/N the value of each. (N 10 W resistor Req=10/N W) What is the effective total resistance when 10 equal 10 W resistors are connected in parallel? What is the effective total resistance when 10 equal 10 W resistors are connected in parallel? Req=10 W/10=1.0 W 20 WResistors are connected in parallel to a 20 V battery. What is the voltage difference across each resistor? Two 20 WResistors are connected in parallel to a 20 V battery. What is the voltage difference across each resistor? Two V=V1=V2=20 V 20 WResistors are connected in parallel to a 20 V battery. What is the current flowing through each resistor? Two 20 WResistors are connected in parallel to a 20 V battery. What is the voltage difference across each resistor? I=V/R I1=V1/R1 and I2=V2/R2 I1=20V/ 20 W=1.0 A I2=20V/ 20 W=1.0 A Two 20 WResistors are connected in parallel to a 20 V battery. What is the total effective resistance of this circuit? Two 20 WResistors are connected in parallel to a 20 V battery. What is the current flowing through each resistor? Two R=V/I=20V/2.0A=10 W