Chapter 16 Electric Current and Circuits 1 Electric Current Electron flow: Conventional current (is the direction of current (I) and is not necessarily the same as the direction of moving charges) _ + higher potential Electron flow • • the free electrons in metals cause the conduction of electricity in the presence of potential difference, electrons will move from negative end to positive end with higher potential Electric current is the motion of charge (positive) from one point to another and is defined as: dQ I= dt net charge passing through an area per unit time Unit of I : Ampere or A (current is not a vector) 2 The moving charges in metals are always electrons (negative charge). In an ionized gas/solution, the moving charges include electrons (negative) and charged ions (positive). Same current is produced by the +ve and –ve charges if number of charges and drifting velocity are the same I I direction of v same as E - v v + E E + v v - direction of v opposite to E v : drift velocity of the charged particle battery _ + I I + 3 Ohm’s Law: the electric current passing through a fixed conductor at constant temperature is proportional to the potential difference between the start and end points of the conductor. V = IR Where, V = potential difference between the start and end points of the conductor [volt or V]; I = current passing through the conductor [Ampere or A]; and R = the resistance of the conductor [ohm or Ω]. Current is not a vector. However, current moves in one direction along a conductor. When a direction is defined as +ve, the opposite direction is –ve or clockwise around a circuit is +ve and counter-clockwise is –ve. 4 Resistance of a conductor (R): R= ρL A Where, R = resistance [Ω]; ρ = resistivity of the metal of which the conductor is made of (a constant for a particular metal) and is a function of temperature (T); A = cross-sectional area of the metal wire [m2]; and L = length of the metal wire [m]. ρ = ρ (T ) ρT = ρ 0 (1 + αT ) Where, neglecting the thermal expansion of the metal RT = R0 (1 + αT ) The reciprocal of resistivity is conductivity (unit: Ω-1 m-1) ρ0 = resistivity of the metal at temperature = 0oC [Ωm]; ρT = resistivity of the metal at temperature = ToC [Ωm]; and α = temperature coefficient of the metal [(Co)-1] . 5 Resistance in series: I A R R 1 2 V1 V2 B The current passing through each resistor is the same V = V1 + V2 = IR1 + IR2 R = R1 + R2 6 Resistance in parallel: I1 R 1 I I2 A R B The potential difference between A and B must be the same 2 V I = I1 + I 2 V I1 = R1 V and I 2 = R2 1 I 1 1 = = + R V R1 R2 7 Electric circuit: the conducting path forming a closed loop where the charge moves. Direct current (DC) circuit: a circuit with the direction of current not changing with time. Alternative current (AC) circuit: a circuit with the direction of current oscillating back and forth. Electromotive force (emf): the influence causing the current flow moving from lower potential to higher potential, e.g. water pump, cells ideal emf : V12 = emf or E E = V12 = IR {unit: volt] R R1 R2 R3 E1 E2 E3 + R = R1 + R2 + R3 E = E1 + E2 + E3 E Single cell cell connected in series 8 Examples of sources of emf: • • • batteries electric generators solar cells, etc. Through the connection of a source of emf, electrical potential energy is transferred into the electric circuit. An ideal source of emf has a constant potential difference between its terminals and is independent of the current passing through it. emf can be defined as the magnitude of the potential difference. Vab = IR = ε Vab = IR = ε − Ir Ideal source of emf Source of emf with internal resistance I : current; r: internal resistance of the emf 9 Kirchhoff’s Rules: Junction rule: • the algebraic sum of the currents passing through any junction is zero ∑I = 0 At any junction conservation of electric charge Loop rule: • the algebraic sum of the potential differences in any loop is zero. Both emf and resistors can be included in the loop. ∑V = 0 For any closed loop electrostatic force is conservative 10 Junction rule: ∑I = 0 junction I1 + I 2 = I 3 Loop rule: R1 ΣV = 0 + I1 Traveling in counter-clockwise direction: R3 E1 − I1 R1 + I 2 R3 + I 2 R2 − E2 = 0 E1 − E2 = I1 R1 − I 2 R3 − I 2 R2 E1 I2 R2 + E2 11 Sign convention: • travel thru a source from – to +, emf is +ve • travel thru a source from + to -, emf is –ve • travel thru a resistor in the same direction as the current, IR term is –ve (decreasing potential) • travel thru a resistor in the opposite direction as the current, IR term is +ve (increasing potential) R -E + emf R +E - + - E E traveling direction - IR resistor I + R + IR - traveling direction I - R + 12 Example 16.1: Find the emf’s ε1 and ε2 in the circuit as shown in the figure, and find the potential difference of point b relative to point a. 1 Ω 20V + ε1 1.0A 4Ω a 2.0A 6Ω 1Ω + b ε2 1Ω + 2Ω Solution: From the given currents in the diagram, the current through the middle branch of the circuit must be 1.00 A (the difference between 2.00 A and 1.00 A). We now use Kirchhoff’s Rules, passing counterclockwise around the top loop: 20.0V − (1.00 A)( 6.00 Ω + 1.00 Ω) + (1.00 A)( 4.00 Ω + 1.00 Ω) − ε 1 = 0 ⇒ ε 1 = 18.0V . Traveling around the external loop of the circuit, the emf ε2 and Vab are: 20.0V − (1.00 A)(6.00 Ω + 1.00 Ω) − (2.00 A)(1.00 Ω + 2.00 Ω) − ε 2 = 0 ⇒ ε 2 = 7.0V . And Vab = 18 V – (1.00 A)(4.00 Ω + 1.00 Ω) = +13.0 V. 13 Energy and Power in Electric Circuits dW = V12 dQ = V12 Idt dW p= = V12 I dt dQ QI = dt V1 V2 I I 1 2 where, W = work done Q = charge I = current t = time p = power or time rate of energy transfer (Watt or W) V12 = V1 – V2 = potential difference between point 1 and point 2. 14