Factors Affecting Resistance & Power

Resistance Across a Circuit Quick Review: What is resistance? Resistance is what hinders the flow of current.

Resistance Across a Circuit Quick Review: What is resistance? Resistance is what hinders the flow of current. All materials have some resistance. Circuit elements (lights, motors, etc.) have much, much more resistance than the wires, and are often just called ‘resistors’.

Resistance Across a Circuit How do resistors affect circuits? Charges lose energy / potential due to resistance. You can calculate the loss of potential – called voltage drop – due to resistance using Ohm’s Law. V2 – V1 = voltage drop = IR

Resistance in Wires The resistance wires that connect most circuits can be completely ignored! But, in some cases, the wire is designed to have high resistance (and high ‘loss’ of energy to heat), usually by making the wire very very long …

Resistance in Wires The resistance of a conducting wire depends on four main factors: • length (longer = more resistance) • cross-sectional area (thinner = more resistance) • temperature (hotter = more resistance) resistivity of material (ρ – different materials have different values) Resistance of a wire when the temperature is kept constant is: L – length A – cross-sectional area

Resistance in Wires What kind of wire is the best conductor? L – length A – cross-sectional area What kind of wire is the best conductor? If you double the length of a wire, how does the resistance change? If you double the cross sectional area of a wire, how does resistance change?

Resistance in Wires What kind of wire is the best conductor? L – length A – cross-sectional area What kind of wire is the best conductor? A short fat cold wire If you double the length of a wire, how does the resistance change? The resistance doubles. If you double the cross sectional area of a wire, how does resistance change? The resistance is reduced by half.

Example Problem – We Do A copper wire (r = 1.72x10-8 Wm) has a length of 1.67 m and a radius of 1.00 mm. If the wire is connected to a 1.5-volt battery, how much current flows through the wire?

Example Problem – We Do A copper wire (r = 1.72x10-8 Wm) has a length of 1.67 m and a radius of 1.00 mm. If the wire is connected to a 1.5-volt battery, how much current flows through the wire? The current can be found from Ohm's Law, V = IR. The V is the battery voltage, so if R can be determined then the current can be calculated. The first step, then, is to find the resistance of the wire: L = 1.60 m. r = 1.00 mm r = 1.72x10-8 Wm, copper - books                           The resistance of the wire is then: R = r L/A = (1.72x10-8 Wm)(1.67)/(3.14x10-6m2 ) = 9.2 W The current can now be found from Ohm's Law: I = V / R = 1.5 / 9.2 = 0.16 A

Electric Power Electric power is the rate at which … …energy is supplied to or used by a device OR … electric energy is converted into another form such as mechanical energy, heat, or light.

Electric Power Electric power is the rate at which … …energy is supplied to or used by a device OR … electric energy is converted into another form such as mechanical energy, heat, or light. Where is that energy coming from? This energy is equal to the potential energy lost by the charges as they move through the circuit elements

Electric Power Power is measured in J s-1 called watts W. Electric power is the rate at which … …energy is supplied to or used by a device OR … electric energy is converted into another form such as mechanical energy, heat, or light. Where is that energy coming from? This energy is equal to the potential energy lost by the charges as they move through the circuit elements Power is measured in J s-1 called watts W.

Electric Power Power is measured in J s-1 called watts W. Electric power is the rate at which … …energy is supplied to or used by a device OR … electric energy is converted into another form such as mechanical energy, heat, or light. Where is that energy coming from? This energy is equal to the potential energy lost by the charges as they move through the circuit elements Power is measured in J s-1 called watts W. What does a 60W light bulb mean? -- It converts electrical energy into light/heat energy at a rate of 60 J per second.

Deriving expressions for determining power Basic definition of power: Remember: W = qV → and I = q/t, so P = I V P = IV P= V2/R P= I2 R

Electric Power – We Do How much current is drawn by a 60 Watt light bulb connected to a 120 V power line? What is the resistance of the bulb?

Electric Power – We Do How much current is drawn by a 60 Watt light bulb connected to a 120 V power line? P = 60 W = I V = I x 120 so I = 0.5 A What is the resistance of the bulb? I = V/R R = V/I = 120 V/0.5 A R = 240 

Electric Power – You Do Calculate the resistance and the current of a 1500-Watt electric hair dryer plugged into a US household outlet (120 V). 2. The sticker on a compact disc player says that it draws 288 mA of current when powered by a 9 Volt battery. What is the power (in Watts) of the CD player?

Electric Power – You Do Calculate the resistance and the current of a 1500-Watt electric hair dryer plugged into a US household outlet (120 V). I = P / V = (1500 W) / (120 V) I = 12.5 Amp R = V / I= (120 V) / (12.5 Amp) R = 9.6 2. The sticker on a compact disc player says that it draws 288 mA of current when powered by a 9 Volt battery. What is the power (in Watts) of the CD player? P = I • V = (0.288 A) • (9 V) P = 2.59 W

Paying for electricity You pay for electricity by the Kilowatt-hour (kWh). What is a kWh? Simply another unit for energy.

Paying for electricity You pay for electricity by the Kilowatt-hour (kWh). What is a kWh? Simply another unit for energy. Physicists measure energy in joules, but utility companies customarily charge energy in units of kilowatt-hours (kW h), where : Kilowatt-hour (kWh) = 1000 W x 3600 s 1W x 1s = 1J 1 kWh = 3.6 x 106 J

Paying for electricity You pay for electricity by the Kilowatt-hour (kWh). What is a kWh? Simply another unit for energy. Physicists measure energy in joules, but utility companies customarily charge energy in units of kilowatt-hours (kW h), where : Kilowatt-hour (kWh) = 1000 W x 3600 s 1W x 1s = 1J 1 kWh = 3.6 x 106 J At a rate of 14 cents per kWh, how much does it cost to keep a 100 W light bulb on for one day? energy (kWh) = power (kW) x time (h) energy (kWh) = 0.1 kW x 24 h = 2.4 kWh cost / day = 2.4 kWh x 14 cents/kWh = 33.6 ¢  for one month that amounts to $ 10.1.