Chapter 27 Current And Resistance

Electric Current Electric current is the rate of flow of charge through some region of space The SI unit of current is the ampere (A) 1 A = 1 C / s The symbol for electric current is I

Instantaneous Electric Current If the rate at which the charge flows varies with time, the instantaneous current, I, can be found

Direction of Current The charges passing through the area could be positive or negative or both It is conventional to assign to the current the same direction as the flow of positive charges The direction of current flow is opposite the direction of the flow of electrons It is common to refer to any moving charge as a charge carrier

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 nAΔx is the total number of charge carriers

Current and Drift Speed, cont The total charge is the number of carriers times the charge per carrier, q ΔQ = (nAΔx)q The drift speed, v d, is the speed at which the carriers move v d = Δx / Δt and  x = v d  t Rewritten: ΔQ = (nAv d Δt)q Finally, current, I ave = ΔQ/Δt = nqv d A

구리 도선 내의 유동 속력예제 27.1 옥내 배선용으로 많이 사용하는 게이지 번호 12 번 구리 도선의 단면적은 3.31 × m 2 이다. 이 도선에 10.0A 의 전류가 흐른다면 도선 내 전자의 유동 속력은 얼마이겠는가 ? 구리 원자 한 개당 전류에 기여하는 자유 전자가 한 개라고 가정한다. 구리의 밀도는 8.92g/cm 3 이다. 풀이 구리 원자 하나당 자유 전자가 하나씩 있다고 가정하면

유동속력 구하기 ▶ 구리 도선의 반지름 ▶ 원자당 하나의 자유전자를 만든다고 가정할 때 1A 의 전류가 흐르는 도선에서 전자의 유동속력은 ? * 매우 느린 속력이지만 도선 안에 전자가 이미 가득 차 있으므로, 스위치를 켜는 순간 도선의 모든 부분에서 전류가 흐르고 순간적으로 전구에 불이 들어오게 된다. 광속 c 로 생성 예제 27.1’

Current Density J is the current density of a conductor It is defined as the current per unit area J = I / A = nqv d This expression is valid only if the current density is uniform and A is perpendicular to the direction of the current J has SI units of A/m 2 The current density is in the direction of the positive charge carriers

Conductivity A current density and an electric field are established in a conductor whenever a potential difference is maintained across the conductor For some materials, the current density is directly proportional to the field The constant of proportionality, σ, is called the conductivity of the conductor

Ohm’s Law Ohm’s law states that for many materials, the ratio of the current density to the electric field is a constant σ that is independent of the electric field producing the current Most metals obey Ohm’s law Mathematically, J = σ E Materials that obey Ohm’s law are said to be ohmic

Ohm’s Law, cont. Not all materials follow Ohm’s law Materials that do not obey Ohm’s law are said to be nonohmic Ohm’s law is not a fundamental law of nature Ohm’s law is an empirical relationship valid only for certain materials

Georg Simon Ohm German physicist Formulated idea of resistance Discovered the proportionalities now known as forms of Ohm’s Law

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 called the resistance of the conductor

Resistance, cont. SI 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

Resistivity The inverse of the conductivity is the resistivity: ρ = 1 / σ Resistivity has SI units of ohm-meters (Ω. m) Resistance is also related to resistivity:

22 게이지 니크롬선의 반지름은 0.321mm 이다. 22 게이지 니크롬선 ; 면적 0.324mm 2, 비저항 ρ=1.5x10 -6 Ω·m 예제 27.2 (A) 단위 길이당 저항 =? (B) 길이 1m, 전위차 10V 일 때 전류 =?

Resistance of a Cable, Example Assume the silicon between the conductors to be concentric elements of thickness dr The resistance of the hollow cylinder of silicon is 예제 27.3

Resistance of a Cable, Example, cont. The total resistance across the entire thickness is This is the radial resistance of the cable This is fairly high, which is desirable since you want the current to flow along the cable and not radially out of it 예제 27.3

Resistance and Temperature Over a limited temperature range, the resistivity of a conductor varies approximately linearly with the temperature ρ o is the resistivity at some reference temperature T o T o is usually taken to be 20° C α is the temperature coefficient of resistivity  SI units of α are o C -1

Temperature Variation of Resistance 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 R = R o [1 + α(T - T o )] Use of this property enables precise temperature measurements through careful monitoring of the resistance of a probe made from a particular material

Electrical Power Assume a circuit as shown As a charge moves from a to b, the electric potential energy of the system increases by Q  V The chemical energy in the battery must decrease by this same amount Use the active figure to adjust the voltage or resistance, observe current and power PLAY ACTIVE FIGURE collisions of the electrons with the atoms of the resistor

Electrical Power, 2 As the charge moves through the resistor (c to d), the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor This energy is transformed into internal energy in the resistor Corresponds to increased vibrational motion of the atoms in the resistor

Electric Power, 3 The resistor is normally in contact with the air, so its increased temperature will result in a transfer of energy by heat into the air The resistor also emits thermal radiation After some time interval, the resistor reaches a constant temperature The input of energy from the battery is balanced by the output of energy by heat and radiation

Electric Power, 4 The rate at which the system loses potential energy as the charge passes through the resistor is equal to the rate at which the system gains internal energy in the resistor The power is the rate at which the energy is delivered to the resistor

Electric Power, final The power is given by the equation: Applying Ohm’s Law, alternative expressions can be found: Units: I is in A, R is in Ω, V is in V, and is in W 1watt=1J/s

예제 27.4 니크롬 열선 저항 8Ω 을 120V 에 연결했다. (A) 전류와 전력 =? (B) 240V 에 연결했을 때전류와 전력 =?

예제 27.5 (B) 물을 끓이는 비용은 =? (100 원 /1kWh) 물 1.5kg 을 전기히터로 가열해서 10 ℃에서 50 ℃로 10 분 만에 끓이고자 한다. 전압은 110V 이다. 10 분 동안 히터를 통해 공급해준 에너지 물 1.5kg 이 10 ℃에서 50 ℃로 더워지는데 필요한 열에너지 (A) 히터의 저항값은 ?

전기와 열역학을 연결해 보기예제 27.5 물 속에 넣어서 물을 끓이는 전기 히터를 사용해서 물 1.50 kg 을 10.0°C 에서 50.0°C 로 10.0 분 만에 물을 끓이고자 한다. 전기 히터의 사용 전압은 110V 이다. (A) 저항값이 얼마인 히터를 사용해야 하겠는가 ? 풀이 분석을 간단히 하기 위해 저항기의 온도가 증가하는 처음 과정을 무시하기로 한다. 그러므로 10.0 분 동안의 에너지 전달률은 일정하다고 하자. (B) 물을 끓이는 비용을 구하라.

100W 전등에 대해 100V 를 걸었을 때 전등에 흐르는 전류는 ? 100W 전등에 대해 200V 를 걸었을 때 전등에 흐르는 전류는 ? 송전하는 구리 전선에서 소모되는 전기에너지는 어디가 적은가 ? 송전하는 구리 전선에서 소모되는 전기에너지는 이므로 200V 송전선에서 소모되는 전기에너지가 더 적다. 200V 는 고전압이므로 위험도는 더 높다.