Current and Resistance Chapter 2 Current and Resistance 11-10-2017 FCI

Objectives : Define the current. Understand the microscopic description of current. Discuss the rat at which the power transfer to a device in an electric current. FCI 11-10-2017

2- Current and Resistance (Ch 27 in serway) 2-1 Electric current 2-2 Resistance and Ohm’s Law 2-3 Current density, conductivity and resistivity 2-4 Electrical Energy and Power FCI 11-10-2017

2-1 Electric Current Whenever electric charges of like signs move, an electric current is said to exist. The current is the rate at which the charge flows through this surface Look at the charges flowing perpendicularly to a surface of area A The SI unit of current is Ampere (A) 1 A = 1 C/s FCI 11-10-2017

∆Q is the amount of charge that passes through this area in a time interval ∆ t, the average current Iav is equal to the charge that passes through A per unit time We define the instantaneous current I as the differential limit of average current: FCI 11-10-2017

Electric Current, cont The direction of the current is the direction positive charge would flow This is known as conventional current direction In a common conductor, such as copper, the current is due to the motion of the negatively charged electrons It is common to refer to a moving charge as a mobile charge carrier . A charge carrier can be positive or negative. For example, the mobile charge carriers in a metal are electrons. FCI 11-10-2017

Current and Drift Speed Charged particles move through a conductor of cross- sectional area A n is the number of charge carriers per unit volume n A Δx is the total number of charge carriers FCI 11-10-2017

Current and Drift Speed, cont The total charge is the number of carriers times the charge per carrier, q ΔQ = (n A Δx) q The drift speed, vd, is the speed at which the carriers move vd = Δx/ Δt Rewritten: ΔQ = (n A vd Δt) q Finally, current, I = ΔQ/Δt = nqvdA OR the average current in the conductor FCI 11-10-2017

Current and Drift Speed, final If the conductor is isolated, the electrons undergo random motion When an electric field is set up in the conductor, it creates an electric force on the electrons and hence a current FCI 11-10-2017

Charge Carrier Motion in a Conductor: The zig-zag black line represents the motion of charge carrier in a conductor The net drift speed is small The sharp changes in direction are due to collisions The net motion of electrons is opposite the direction of the electric field FCI 11-10-2017

2-2 Resistance Consider a conductor of cross-sectional area A carrying a current I. The current density J in the conductor is defined as the current per unit area. Because the current I = nqvdA, the current density is: the current density is proportional to the electric field: Where σ the constant of proportionality & is called the conductivity of the conductor. FCI 11-10-2017

and If the field is assumed to be uniform, the potential difference is related to the field through the relationship express the magnitude of the current density in the wire as FCI 11-10-2017

Where ,J = I/A, we can write the potential difference as The quantity R = ℓ/σA is called the resistance of the conductor. We can define the resistance as the ratio of the potential difference across a conductor to the current in the conductor: FCI 11-10-2017

The resistance R of an element denotes its ability to resist the flow of electric current; it is measured in ohms. The resistance of any material is dictated by four factors: 1. Material property—each material will oppose the flow of current differently. 2. Length—the longer the length , the more is the probability of collisions and, hence, the larger the resistance. 3. Cross-sectional area—the larger the area A, the easier it becomes for electrons to flow and, hence, the lower the resistance. 4. Temperature—typically, for metals, as temperature increases, the resistance increases FCI 11-10-2017

Thus, the resistance R of any material with a uniform cross- sectional area A and length (as shown in Fig) is directly proportional to the length and inversely proportional to its cross-sectional area. In mathematical form, FCI 11-10-2017

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Quiz 1: A cylindrical wire has a radius r and length L Quiz 1: A cylindrical wire has a radius r and length L. If both r and L are doubled, the resistance of the wire, (a) increases (b) decreases (c) remains the same. FCI 11-10-2017

SOLUTION: (b) decreases The doubling of the radius causes the area A to be four times as large, so tells us that the resistance decreases. FCI 11-10-2017

Example 1: FCI 11-10-2017

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Resistance In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductor The constant of proportionality is the resistance of the conductor FCI 11-10-2017

Resistance, Units of resistance are ohms (Ω) 1 Ω = 1 V / A Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor FCI 11-10-2017

2-2 Ohm’s Law Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents This statement has become known as Ohm’s Law ΔV = I R Ohm’s Law is an empirical relationship that is valid only for certain materials Materials that obey Ohm’s Law are said to be Ohmic FCI 11-10-2017

Ohm’s Law, cont An ohmic device The resistance is constant over a wide range of voltages The relationship between current and voltage is linear The slope is related to the resistance FCI 11-10-2017

Ohm’s Law, final Non-Ohmic materials are those whose resistance changes with voltage or current The current-voltage relationship is nonlinear A diode is a common example of a non-Ohmic device FCI 11-10-2017

Summary The electric current I in a conductor is defined as The average current in a conductor is related to the motion of the charge carriers through the relationship The magnitude of the current density J in a conductor is the current per unit area: The current density in an ohmic conductor is proportional to the electric field according to the expression FCI 11-10-2017

The resistance R of a conductor is defined as where ∆V is the potential difference across it, and I is the current it carries. For a uniform block of material of cross sectional area A and length L, the resistance over the length L is where ρ is the resistivity of the material. FCI 11-10-2017