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AP Physics III.C Electric Circuits III.C.1 Current, Resistance, Power The shortcomings of electrostatics EMF – a gross misnomer. Simply the potential difference of the circuit Ex. The amount of charge that passes through the filament of a certain light bulb is 1.67 C in 2.00 s. Find the a) current and b) the number of electrons that pass through the filament in 1.00 s. Conventional current • Hypothetical flow of positive charge • Consistent with positive test charge and electric fields • Always goes from higher potential to lower potential Ohm’s Law An analogy to water Resistance and Resistivity Comparison to water again. Resistivity is a property of a given material. Resistance depends on resistivity and geometry. Concept check: a piece of copper wire has resistance R. In terms of R, what is the resistance R’ of a second piece of copper wire that is twice as long, and half the diameter of the first? Electric Power A couple of derivations Ex. An electric heater is operated by applying a potential difference of 20.0 V to nichrome wire for a total resistance of 4.00 Ohms. Find the current in the wire and the power dissipated by the heater. How much does it cost to run the heater for 8 hours each day for three days if the cost per kwh is $0.13? III.C.2 Series, Parallel and Combination Circuits Series circuit – all devices are connected in such a way that there is the same current through each device. In series wiring the potential difference is divided (potential drop) among the resistors. Equivalent resistance for a series circuit Equivalent resistance for a series circuit (note the largest resistor has the greatest effect on the equivalent resistance for a series circuit) Note: the power in a series circuit can be found from the sum of the powers delivered to the individual resistors, or the power delivered to the equivalent resistance. Ex. For the circuit below, find a) the equivalent resistance b) the current in each resistor c) the potential difference across each resistor d) the power dissipated by each resistor and e) the power dissipated by the circuit. Internal resistance The internal resistance r is connected in series with the external resistance R. r causes the potential difference between the terminals to drop below the maximum EMF. This actual voltage is the terminal voltage. Ex. For the circuit shown find the a) current drawn from the battery b) the terminal voltage of the battery and c) the potential difference across each external resistor. Parallel Circuits Parallel circuit – a circuit wired in such a way that the same voltage is applied across each resistor. Pondering the equivalent resistance of a parallel circuit. For parallel circuits, the smallest resistor has the greatest effect on the equivalent resistance. This explains a short circuit. Ex. For the circuit shown find the a) current in each resistor and b) the total power dissipated by the three resistors. Ex. Three resistors with resistances of 20.0 Ohms, 40.0 Ohms and an unknown resistance are connected in parallel to a battery with a potential difference of 24.0 V. The current in the battery is 3.00 A. Find a) the equivalent resistance b) the unknown resistance and c) the current in the unknown resistor. Ex. For the circuit shown find a) the potential difference across the battery b) the current in the 12 Ohm resistor c) the current in the unknown resistor d) the equivalent resistance and e) the power dissipated by each resistor. Summary of Series and Parallel Circuits • Current • Resistance • Potential difference Combination Circuits Ex. For the circuit shown, find a) the current in the circuit b) the potential difference across each resistor and c) the current in each resistor. Ammeters and voltmeters Brightness (an intelligence component greatly lacking in the students in this class) For the bulbs shown: a) compare the brightness of each bulb when the switch is closed b) and the brightness of B and C when the switch is open. Is C more, less or have the same brightness when the switch is open compared to when it is closed? Parallel Plate Capacitors Charging a Capacitor Capacitors in Circuits Capacitors in Parallel CP = C1 + C2 + C3 + . . . So, adding capacitors in parallel increases the equivalent capacitance. Why? Adding capacitors in series reduces the equivalent capacitance. Why? Summary for capacitors in circuits • Parallel – potential difference is the same across each capacitor, the charge on each capacitor may differ • Series – the charge on each capacitor is the same, but there is a voltage drop across each capacitor RC-circuits • Immediately after the switch of an RCcircuit is closed, the capacitor is treated as a wire with no resistance • After the switch has been closed a long time, the capacitor is treated as broken wire Ex. (Princeton Review) Determine the current through and the voltage across each electrical device in the circuit when a) just after the switch is closed and b) the switch has been closed for a long period of time. Ex. (Princeton Review) Determine the current through and the voltage across each electrical device in the following circuit when a) the switch has been closed and b) the switch has been closed a long time.