• Draw a circuit with resistors in parallel and in series.
• Calculate the voltage drop of a current across a resistor using Ohm’s law.
• Contrast the way total resistance is calculated for resistors in series and in parallel.
• Explain why total resistance of a parallel circuit is less than the smallest resistance of any of the resistors in that circuit.
• Calculate total resistance of a circuit that contains a mixture of resistors connected in series and in parallel.
Resistors in series. Major features of resistors in series.
Example 21.1 Calculating resistance, current, voltage drop, and power dissipation: Analysis of a series circuit.
Resistors in parallel. Major features of resistors in parallel.
Example 21.2 Calculating resistance, current, power dissipation, and power output: Analysis of a parallel circuit.
Combination of series and parallel. Practical implications.
Example 21.3 Calculating resistance, IR drop, current, and power dissipation: Combining series and parallel circuits.
Resistors in Series: (For example, see internal resistance of a battery.)
Resistors in Parallel:
Combination Circuits. A complex resistor network may often be analyzed by the series and parallel combination rules to give one equivalent resistance . More complicated networks can always be analyzed using Kirchhoff’s Rules…
• Compare and contrast the voltage and the electromagnetic force of an electric power source.
• Describe what happens to the terminal voltage, current, and power delivered to a load as internal resistance of the voltage source increases (due to aging of batteries, for example).
• Explain why it is beneficial to use more than one voltage source connected in parallel.
Electromotive force. Internal resistance. Terminal voltage.
Example 21.4 Calculating terminal voltage, power dissipation, current, and resistance: Terminal voltage and load.
Multiple voltage sources. Animals as electrical detectors. Solar cell arrays.
Batteries and Electromotive Force. A battery uses an energy source to produce an electric potential between its two terminals. The potential generated by a battery in the absence of a load (open terminals) is called its electromotive force ℰ or
EMF. It has the same units as electric potential. As it moves a charge from one terminal to the other, the battery does work . When the battery’s internal resistance is taken into account, the terminal voltage is .
• Analyze a complex circuit using Kirchhoff’s rules, using the conventions for determining the correct signs of various terms.
Junction rule. Loop rule. Applying Kirchhoff’s rules.
Example 21.5 Calculating current: Using Kirchhoff’s rules.
The Junction Rule: The algebraic sum of all the currents meeting at (flowing into) any junction in a circuit must equal zero.
This guarantees that electric charge is conserved. I.e., Note that, if some currents are assumed to flow into the junction, while others are assumed to flow out of the junction, we have, e.g.,
The Loop Rule: The algebraic sum of all potential differences around any closed loop in a circuit is zero. This includes battery
EMFs, and guarantees that the potential is well-defined at any point. I.e.,
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21.4 DC Voltmeters and Ammeters
21.5 Null Measurements
21.6 DC Circuits Containing Resistors and Capacitors
Glossary / Section Summary / Conceptual Questions / Problems and Exercises