Lecture Notes

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Topics: RC circuit
Lecture Notes for Analog Electronics

Raymond E. Frey
Physics Department
University of Oregon
Eugene, OR 97403, USA rayfrey@cosmic.uoregon.edu December, 1999

Class Notes 1

1

Basic Principles

In electromagnetism, voltage is a unit of either electrical potential or EMF. In electronics, including the text, the term “voltage” refers to the physical quantity of either potential or
EMF. Note that we will use SI units, as does the text.
As usual, the sign convention for current I = dq/dt is that I is positive in the direction which positive electrical charge moves.
We will begin by considering DC (i.e. constant in time) voltages and currents to introduce
Ohm’s Law and Kirchoﬀ’s Laws. We will soon see, however, that these generalize to AC.

1.1

Ohm’s Law

For a resistor R, as in the Fig. 1 below, the voltage drop from point a to b, V = Vab = Va − Vb is given by V = IR.

I a b
R

Figure 1: Voltage drop across a resistor.

A device (e.g. a resistor) which obeys Ohm’s Law is said to be ohmic.
The power dissipated by the resistor is P = V I = I 2 R = V 2 /R.

1.2

Kirchoﬀ’s Laws

Consider an electrical circuit, that is a closed conductive path (for example a battery connected to a resistor via conductive wire), or a network of interconnected paths.
1. For any node of the circuit in I = out I . Note that the choice of “in” or “out” for any circuit segment is arbitrary, but it must remain consistent. So for the example of
Fig. 2 we have I1 = I2 + I3 .
2. For any closed circuit, the sum of the circuit EMFs (e.g. batteries, generators) is equal to the sum of the circuit voltage drops: E = V .
Three simple, but important, applications of these “laws” follow.

1

I3

I1

I2

Figure 2: A current node.

1.2.1

Resistors in series

Two resistors, R1 and R2 , connected in series have voltage drop V = I (R1 + R2 ). That is, they have a combined resistance Rs given by their sum:
Rs = R1 + R2 n i=1

This

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