1 It is essential to specify reference directions for current and voltage + - V(t) i(t) Voltage and current are algebraic quantities and the signs are critical.

2 Resistors are very common circuit elements What is their function ?

3 Resistors obey Ohm’s law. Note the convention on reference directions: For passive elements, current flows into the positive terminal i(t) + _ v(t) R

4 For passive elements, current flows into the positive terminal i(t) + _ v(t) R

5 In a resistor, voltage is directly proportional to current i v R = slope

6 Ohm’s law in action: example i (mA) R = 1k  V 1 2

7 A resistor can also be characterized by a quantity called conductance (G). i(t) = G v(t) v i G = slope     1  1 G is of Unit mho

8 Resistance can be readily calculated for geometric figures with constant cross-section A L =R  The units of resistance is ohms (   = Conductivity (  m  L = Length of the cylinder ( m ) A = Area of the cylinder ( m 2 ) L  A

9 Resistance is proportional to length and inversly proportional to the cross sectional area Resistance depends on the material Long wires have large resistance Thick cross section bars will have low resistance L  A

10 Copper wires have very low resistance R= L A  L 0.3 m A  m 2      35 R  However, if L  3 km  3.5 R  m

11 For an ideal voltage source, voltage is independent of current V I Reference current convention of a voltage source is arbitrary v (t) + _

12 Examples of voltage sources DC AC Pulsed Ramp time voltage

13 In an ideal current source, current is independent of voltage V I i(t)