CHAPTER-26

Current and

Resistance

Ch 26-2 Electric Current

Electric Current: Motion of conduction electrons under the effect of an E field in the conductor

Fig (a) loop of wire in electrostatic equilibrium, E=0 no current

Fig (b) loop connected to a battery- E 0 in the loop electrons move in the direction opposite to current i

Ch 26-2 Electric Current

Ch 26-2 Electric Current

Current is scalar quantity Junction point: a point where a current split

into two or more currents or two or more currents merge into one current

Current entering the junction is equal to current leaving the junction : i0=i1+i2

Current Density J: a vector quantity; magnitude of J given by current i per unit cross section area A of a conductor then:

J=i/A ; i= J.dA= JdA cos i = JdA= JdA= JA Direction of J : parallel to i

Ch 26-3 Current Density

Random speed: Speed of electrons in random motion in the absence of an E-field electrons with zero net motion

random speeds 106 m/s Drift Speed Vd : in the presence

of an E-field electrons move randomly with net motion in the direction opposite to E field

Drift speed Vd 10-5 - 10-4 m/s

J=(ne)vd

where ne is carrier charge density: +ve for positive carrier and -ve of electrons

Ch 26-4 Resistance and Resistivity

Resistance R : ratio of applied voltage V across a conductor to the current resulting through the conductor R= V/i

Unit of resistance Ohm (): 1 = 1V/1A; i=V/R

if we consider electric field E in a conductor then we deal with J and resistivity instead of i and R respectively :

J= E / ; = E/J; E= J

Calculating Resistance from Resistivity = E/J=(V/l)/(i/A)=(V/i)(A/l); = R A/l; R= A/l

Variation of resistance with Temperature:

=T-0= 0 (T-T0), where is temperature coefficient of resistivity.

Ohm’s law- An assertion: Current through a device directly proportional to the potential difference across the device

Ch 26-5 Ohm’s Law

Ch 26-5 Power in Electric Circuit A resistor connected across

points a and b in the circuit. Battery maintains a potential difference of V between its terminal and a current i in the circuit.

The amount of charge dq moved through a and b in time dt is dq= idt

Since charge moves from +ve to –ve terminal, its potential energy U decreases by U=dqV=i dtV.

Power P associated with this energy dissipation is

P=dU/dt =iV=i2R=V2/R

Thank you