In this course our discussion of circuits will be limited to just a few aspects. The simplest circuit consists of a source of emf (ac or dc), a resistor and some wire to connect them together. We will closely examine the effects on a circuit of resistors that are networked in series and in parallel. We will explore the nature of the wire that connects them to each other and briefly discuss the sorts of phenomena that produce the emf. We will look at various types of resistors: lamp filaments, heating elements, motors etc.
Series Circuits
Charge flows along a continuous, undivided path at an equal rate through all components.
Potential drops occur at each resistance. The ratio of the potential drop across a particular resistance to the open cell potential of the cell is the same as the ratio of the resistance value of the particular resistor to the total resistance of the circuit.
Another way to say this is to say that the sum of the changes in potential for any continuous loop of a circuit must be zero. If a single cell or battery provides a positive change in potential then each resistor hosts a negative change in potential where the sum of several would exactly sum to zero when added to the cell potential.
In analyzing series circuit the chief advantages come when realizing that the current, I is first of all equal to the total potential imparted across the circuit divided by the total resistance of the circuit and second of all that the current is the same through each and every element of the circuit. The potential difference (drop) at any particular resistance is therefore: Δ V= IR.
Parallel Circuits
In a parallel circuit there are junctions, and at junctions the current will divide. The junction rule requires that the current into a circuit must equal the current out of that same junction (a simple junction cannot store charge, even for an instant). As each branch of a parallel network starts at the same potential and ends at the same potential, it is necessarily true that the potential drop across any resistor in the network is the same as in any of the others -- no matter how many or what value of resistance.
Other Components
We will take an extended look at an additional circuit element, the capacitor. We will explore its theoretical underpinnings and examine its role in various circuits.
Other circuit components such as inductors, diodes and transistors will have only brief consideration in this course.