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Electric Currents Physics Department, New York City College of Technology

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Key words Electric battery Electric current Resistance Ohm’s law Resistivity Electric energy Electric power Direct current Alternating current Average power rms values

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Electric battery A battery produces electricity by transforming chemical energy into electrical energy.

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Electric battery In a diagram of a circuit, it is denoted by the symbol +

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Electric current Electric current is a flow of charge

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Electric current Current is defined as I is current ∆Q is the amount of charge that passes through the conductor at any location Δt is the time interval The unit of I is ampere (A)

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Direction of electric current

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Electrical resistance Defined as R is the resistance of a wire V is the potential difference applied across the wire I is the current The symbol of a resistor is

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Electron motion model Disc 17, #22

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Ohm’s law Resistance R is a constant independent of V, i.e., Experimentally found by Ohm Generally holds in metal conductors in room temperature

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Ohm’s law Disc 17, #19 Disc 17, #20 Disc 17, #21

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Resistivity It is experimentally found that ρ is resistivity and depends on the material L is the length of a wire A is the cross-sectional area

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Resistivity

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Example #1 A flashlight bulb draws 300mA from its 1.5-V battery. (a) What is the resistance of the bulb? (b) If the battery becomes weak and voltage drops to 1.2V, how would the current change?

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Example #1—continued (a) (b)

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Example #2 Connect stereo to speakers. (a) If each wire must be 20m long, what diameter copper wire should be used to keep the resistance less than 0.10 Ω? (b) If the current is 4.0A, what is the potential difference across each wire?

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Example #2—continued (a) (b)

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Electric energy Energy transformation between electric and other forms are very common Motors transform electric energy into mechanical energy In electric heaters and hair dryers, electric energy is transformed into thermal energy In a lightbulb, electric energy is transformed into light and thermal energy

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Electric power The electric power transformed by any device is P is electric power I is current V is potential difference The unit of electric power is Watt (W) For a resistance R, we have

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Example #3 Calculate the resistance of a 40-W automobile headlight designed for 12V.

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Example #3—continued

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Alternating current The voltage and current produced by an electric generator are sinusoidal V 0 is the peak voltage I 0 is the peak current The frequency f is the number of complete oscillations per second, and

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DC and AC

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AC power The power transformed in a resistance R at any instant is The average power is calculated as or

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AC power—continued

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rms (root-mean-square) values rms values and peak values The average power in rms values:

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Example #4 (a) Calculate the resistance and the peak current in a 1000-W hair dryer connected to a 120-V line. (b) What if it is connected to a 240-V line in Britain?

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Example #4 (a) (b)

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