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# Fundamentals of Physics, (Chapters 21- 44) (Volume 2)

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Chapter 27 Circuits In this chapter we will cover the following topics: -Electromotive force (emf) -Ideal and real emf devices -Kirchhoff’s loop rule -Kirchhoff’s junction rule -Multiloop circuits -Resistors in series -Resistors in parallel -RC circuits, charging and discharging of a capacitor (27 – 1)

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In order to create a current through a resistor, a potential difference must be created across its terminals. One way of doing this is to connect the resistor to a battery. A device that can maintain a potential difference between two terminals is called a or an . Here emf stands for: electromotive force. Examples of emf devices: a battery, an electric generator, a so "seat of an emf " "emf device" lar cell, a fuel cell, etc pump High (+) reservoir Low (-) reservoir These devices act like "charge pumps" in the sense that they move positive charges from the low potential (negative) terminal to the high potential (positive) terminal. A mechanical analog is given in the figure below. In this mechanical analog a water pump transfers water from the low to the high reservoir. The water returns from the high to the low reservoir through a pipe which is the analog of the resistor. The emf (symbol ) is defined as the potential difference between the terminals of the emf device when no current flows through it. E (27 – 2)
The polarity of an emf device is indicated by an arrow with a small circle at its tail. The arrow points from the negative to the positive terminal of the device. When the emf device is co Notation : nnected to a circuit its internal mechanism transports positive charges from the negative to the positive terminal and sets up a charge flow (a.k.a. current) around the circuit. In doing so the emf device does work on a charge which is given by the equation: . The required energy comes from chemical reactions in the case of a battery; in the case of a generator it comes from the mecha dW q dq d dW = E nical force that rotates the generator shaft; in the case of a solar cell it comes from the sun. In the circuit of the figure the energy stored in emf device B changes form: It does mechanical work on the motor. It produces thermal energy on the resistor. It gets converted into chemical energy in emf device A (27 – 3)

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An emf device is said to be if the voltage across its terminals and does depend on the current that flows through the emf device. An emf device is s id a V a b i V = Ideal and real emf devices ideal not E to be if the voltage across its terminals and with current according to the equation: . The parameter is known as the device's " " of the emf device V ir V a b i r = ! real decreases internal resistance E . V i E Ideal emf device V i E Real emf device V = E V ir = ! E (27 – 4)
Consider the circuit shown in the figure. We assume that the emf device is ideal and that the connecting wires have negligible resistance. A current flows through the c i Current in a single loop circuit ircuit in the clockwise direction.

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