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# HR26 - Chapter 26 Current and Resistance J In this chapter...

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Chapter 26 Current and Resistance In this chapter we will introduce the following new concepts: -Electric current ( symbol i ) -Electric current density vector (symbol ) J r (26 - 1)

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Consider the conductor shown in fig.a. All the points inside the conductor and on its surface are at the same potential. The free electrons inside the conductor move at random directi Electric current ons and thus there is not net charge transport. We now make a break in the conductor and insert a battery as shown in fig.b. Points A and B are now at potentials and , respectively. ( the A B A B V V V V V - = voltage of the battery) The situation is not static any more but charges move inside the conductor so that there is a net charge flow in a particular direction. This net flow of electric charge we define as "electric currrent" A B (26 - 2)
i + q conductor v r i - q conductor v r Consider the conductor shown in the figure It is connected to a battery (not shown) and thus charges move through the conductor Consider one of the cross sections through the conductor ( aa or bb or c Current = rate at which charge flow c ) The electric current is defined Current SI Unit: C/s known as the "Ampere s s: " a dq i t i d = An electric current is represented by an arrow which has the same direction as the charge velocity. The sense of the current arrow is defined as follows: If the current is due to t Current direction : 1. he motion of charges the current arrow is to the charge velocity If the current is due to the motion of charges the current arrow is to the charge veloci t v parallel 2. ant nega iparallel posit tive ive r y v r (26 - 3) dq i dt =

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i - q conductor v r A J r Current density is a vector that is defined as follows: Its magnitude The direction of is the same as that of the current The current through a condu i J A J = Current density r 2 SI unit for J: A/m ctor of cross sectional area is given by the equation: if the current density is constant. If is not constant then: i JA i J d A J A = = r r r i + q conductor v r A J r 1 We note that even though the current density is a vector the electric current is not. This is illustrated in the figure to the left.
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