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DC circuits Physics Department, New York City College of Technology

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Key words Electromotive force (emf) Terminal voltage Resistors in parallel and in series Kirchhoff’s rules Junction rule Loop rule Capacitors in series and in parallel RC cuicuits

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emf Electromotive force (emf) refers to the potential difference between the terminals of a source when no current flows out. Its symbol is .

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Terminal voltage Terminal voltage is the potential difference between the terminals of a source when current flows, and is calculated as is the emf r is the internal resistance of the battery

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Example #1 A 65-Ω resistor is connected to the terminals of a battery whose emf is 12V and whose internal resistance is 0.5Ω. Calculate (a) the current in the circuit, (b) the terminal voltage of the battery, and (c) the power dissipated in the resistor R and in the battery's internal resistance r.

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Example #1—continued (a) (b) (c)

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Resistors in series The equivalent resistance for resistors in series is

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Resistors in parallel The equivalent resistance for resistors in parallel is

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Voltage drop along wire Disc 18, #1 Disc 18, #2 Disc 18, #6

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Series/parallel resistors Disc 17, #23 Disc 17, #24

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Example #2 Two 100Ω resistors are connected (a) in parallel, and (b) in series, to a 24V battery. What is the current through each resistor and what is the equivalent resistance of each circuit?

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Example #2—continued (a)

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Example #2—continued (b)

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Kirchhoff’s rules The junction rule: at any junction point, the sum of all currents entering the junction must equal the sum of all currents leaving the junction. It is based on the conservation of electric charge. The loop rule: the sum of the changes in potential around any closed path of a circuit must be zero. It is based on the conservation of energy.

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Example #3 Calculate the currents I 1, I 2, and I 3.

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Example #3—continued

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Capacitors in series and in parallel The equivalent capacitance for capacitors in series is The equivalent capacitance for capacitors in parallel is

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RC circuits In the charging process, In the discharging process, The time constant is Switch C R ε

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RC charging curve Disc 18, #28

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