Current and Resistance FCI

 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

 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

 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

 ∆Q is the amount of charge that passes through this area in a time interval ∆ t, the average current I av is equal to the charge that passes through A per unit time 5 We define the instantaneous current I as the differential limit of average current: FCI

 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

 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

 The total charge is the number of carriers times the charge per carrier, q ◦ ΔQ = (n A Δx) q  The drift speed, v d, is the speed at which the carriers move ◦ v d = Δx/ Δt  Rewritten: ΔQ = (n A v d Δt) q  Finally, current, I = ΔQ/Δt = nqv d A  OR 8 the average current in the conductor FCI

 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

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

 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 = nqv d A,  the current density is: 11 the current density is proportional to the electric field: Where σ the constant of proportionality & is called the conductivity of the conductor FCI

 If the field is assumed to be uniform, the potential difference is related to the field through the relationship 12 express the magnitude of the current density in the wire as FCI

 Where,J = I/A, we can write the potential difference as 13 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

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 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

 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

 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

 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

 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

 The resistance of an ohmic conductor is proportional to its length, L, and inversely proportional to its cross-sectional area, A ◦ ρ is the constant of proportionality and is called the resistivity of the material FCI

 For most metals, resistivity increases with increasing temperature ◦ With a higher temperature, the metal’s constituent atoms vibrate with increasing amplitude ◦ The electrons find it more difficult to pass through the atoms FCI

 For most metals, resistivity increases approximately linearly with temperature over a limited temperature range ◦ ρ is the resistivity at some temperature T ◦ ρ o is the resistivity at some reference temperature T o  T o is usually taken to be 20° C   is the temperature coefficient of resistivity FCI

 Since the resistance of a conductor with uniform cross sectional area is proportional to the resistivity, you can find the effect of temperature on resistance FCI

 A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, T C ◦ T C is called the critical temperature  The graph is the same as a normal metal above T C, but suddenly drops to zero at T C

 In a circuit, as a charge moves through the battery, the electrical potential energy of the system is increased by ΔQΔV  As the charge moves through a resistor, it loses this potential energy during collisions with atoms in the resistor ◦ The temperature of the resistor will increase FCI

 Consider the circuit shown  Imagine a quantity of positive charge,  Q, moving around the circuit from point A back to point A FCI

 Point A is the reference point ◦ It is grounded and its potential is taken to be zero  As the charge moves through the battery from A to B, the potential energy of the system increases by Q  V ◦ The chemical energy of the battery decreases by the same amount FCI

 As the charge moves through the resistor, from C to D, it loses energy in collisions with the atoms of the resistor  The energy is transferred to internal energy 33 When the charge returns to A, the net result is that some chemical energy of the battery has been delivered to the resistor and caused its temperature to rise FCI

 The rate at which the energy is lost is the power  From Ohm’s Law, alternate forms of power are FCI

 The SI unit of power is Watt (W) ◦ I must be in Amperes, R in ohms and  V in Volts  The unit of energy used by electric companies is the kilowatt-hour ◦ This is defined in terms of the unit of power and the amount of time it is supplied ◦ 1 kWh = 3.60 x 10 6 J FCI

The same potential difference is applied to the two lightbulbs shown in Figure.Which one of the following statements is true?  (a) The 30-W bulb carries the greater current and has the higher resistance.  (b) The 30-W bulb carries the greater current, but the 60-W bulb has the higher resistance FCI

 (c) The 30-W bulb has the higher resistance, but the 60-W bulb carries the greater current.  (d) The 60-W bulb carries the greater current and has the higher resistance FCI

 (c). Because the potential difference ∆V is the same across the two bulbs and because the power delivered to a conductor is P= I V, the 60-W bulb, with its higher power rating, must carry the greater current.  The 30-W bulb has the higher resistance because it draws less current at the same potential difference FCI

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1. The electric current I in a conductor is defined as where dQ is the charge that passes through a cross section of the conductor in a time interval dt. The SI unit of current is the ampere (A), where 1 A = 1 C/s. The average current in a conductor is related to the motion of the charge carriers through the relationship 41 where n is the density of charge carriers, q is the charge on each carrier, v d is the drift speed, and A is the cross- sectional area of the conductor FCI

2. The current density in an ohmic conductor is proportional to the electric field according to the expression 42 The proportionality constant σ is called the conductivity of the material of which the conductor is made. The inverse of & is known as resistivity ρ (that is, ρ = 1/ σ). The last equation is known as Ohm’s law, and a material is said to obey this law if the ratio of its current density J to its applied electric field E is a constant that is independent of the applied field FCI

43 3. The resistance R of a conductor is defined as where ∆V is the potential difference across it, and I is the current it carries. The SI unit of resistance is volts per ampere, which is defined to be 1 ohm; that is, 1Ω = 1 V/A. If the resistance is independent of the applied potential difference, the conductor obeys Ohm’s law FCI

4. If a potential difference ∆V is maintained across a circuit element, the power, or rate at which energy is supplied to the element, is 44 Because the potential difference across a resistor is given by ∆V = IR, we can express the power delivered to a resistor in the form The energy delivered to a resistor by electrical transmission appears in the form of internal energy in the resistor FCI

1. The charge carriers in metals are A. electrons. B. positrons. C. protons. D. a mix of protons and electrons FCI45

2. A battery is connected to a resistor. Increasing the resistance of the resistor will  A. increase the current in the circuit.  B. decrease the current in the circuit.  C. not affect the current in the circuit FCI46

3. A battery is connected to a resistor. As charge flows, the chemical energy of the battery is dissipated as  A. current.  B. voltage.  C. charge.  D. thermal energy FCI47