Understanding Electric Current: Current Density, Continuity, and Metallic Conductors, Exercises of Engineering

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Currents And Conductor

Department of Electrical Engineering GC University, Lahore Engr Muhammad Salman 14 - BSEE- 15

Contents

1. Current
2. Current Density
3. D 5.
4. Continuity Of Current
5. D 5.
6. Metallic Conductor
7. D 5.
8. D 5.

Electric Current Unit

• The SI and base unit of electric current is Ampere’s
• 𝑎𝑚𝑝𝑒𝑟𝑒 = 𝑐𝑜𝑙𝑢𝑚𝑏 𝑠𝑒𝑐𝑜𝑛𝑑
• 1𝐴 = 1𝐶 1𝑠𝑒𝑐
• 𝐴 = 𝐶𝑠 − 1
• Ampere
• When one coulomb charge flow through any cross sectional area in one second then electric will be one Ampere.

Conti…

• Electric current is taken as scalar
• Electric current is a SCALAR quantity! Sure it has magnitude and direction, but it still is a scalar quantity!
• Confusing? Let us see why it is not a vector as Scalar Quantity.
• First let us define a vector! A physical quantity having both magnitude and a specific direction is a vector quantity.
• Is that all? No! This definition is incomplete! A vector quantity also follows the triangle law of vector addition.

Conti…

• Now consider a triangular loop in an electric circuit with vertices A,B and C.
• The current flows from A→ B, B→C and C→A.
• Now had current been a vector quantity, following the triangle law of vector addition, the net current in the loop should have been zero!
• But that is not the case, right? You wont be having a very pleasant experience if you touch an exposed high current loop

Result

• So current does not follow triangular vector addition that’s why current is a scalar quantity not a vector

Unit

• Unit of electric current density is ampere per meter square.
• 𝐽 = 𝐴𝑚𝑝𝑒𝑟𝑒 𝑚𝑒𝑡𝑒𝑟^2
• Electric current density is a vector quantity.
• Its direction is same as electric current.
• In vector form
• 𝐼 = 𝑱. 𝑨
• 𝐼 = 𝐽𝐴𝐶𝑂𝑆∅ J I

Conti..

• Current density, J, yields current in Amps when it is integrated over a cross- sectional area. The assumption is that the direction of J is normal to the surface, and so we would write:

Relation of Current to Charge Velocity Consider a charge  Q , occupying volume  v , moving in the positive x direction at velocity v In terms of the volume charge density, we may write: x Suppose that in time  t , the charge moves through a distance  x =  L = vx  t The motion of the charge represents a current given by:

Relation of Current Density to Charge Velocity The current density is then: So in general form

 Equation of Continuity:- “The total current flowing out of some volume is equal to the rate of decrease of charge within that volume”.  Let us consider a volume V bounded by a surface S. A net charge Q exists within this region. If a net current I flows across the surface out of this region, from the principle of conservation of

charge this current can be equated to the time rate of decrease of charge within this volume. Similarly, if a net current flows into the region, the charge in the volume must increase at a rate equal to the current. Thus we can write the current through closed surface is

 The above equation is the integral form of the continuity equation, and the differential, or point, form is obtained by using the Divergence Theorem to change the surface integral into volume integral:

 We next represent the enclosed charge Qi by the volume integral of the charge density,  If we agree to keep the surface constant, the derivative becomes a partial derivative and may appear within the integral,