ECE201 Lect-21 Ohm's Law (2.1); Kirchhoff's Laws (2.2) Dr. Holbert January 23, 2006

ECE201 Lect-22 Resistors A resistor is a circuit element that dissipates electrical energy (usually as heat) Real-world devices that are modeled by resistors: incandescent light bulbs, heating elements (stoves, heaters, etc.), long wires Resistance is measured in Ohms (  )

ECE201 Lect-23 Ohm’s Law v(t) = i(t) R- or -V = I R p(t) = i 2 (t) R = v 2 (t)/R[+ (absorbing)] The Rest of the Circuit Rv(t)v(t) i(t)i(t) + –

ECE201 Lect-24 Example: a 25W Bulb If the voltage across a 25W bulb is 120V, what is its resistance? R = V 2 /P = (120V) 2 /25W = 576  What is the current flowing through the 25W bulb? I = V/R = 120V/576  = A

ECE201 Lect-25 Thought Question When I measured the resistance of a 25W bulb, I got a value of about 40 . What’s wrong here? Answer: The resistance of a wire increases as the temperature increases. For tungsten, the temperature coefficient of resistivity is 4.5x10 -3 / o K. A light bulb operates at about 5000 o F.

ECE201 Lect-26 Open Circuit What if R=  ? i(t) = v(t)/R = 0 The Rest of the Circuit v(t)v(t) i(t)=0 + –

ECE201 Lect-27 Short Circuit What if R=0? v(t) = R i(t) = 0 The Rest of the Circuit v(t)=0 i(t)i(t) + –

ECE201 Lect-28 Class Example Learning Extension E2.1(a) Learning Extension E2.2(a)

ECE201 Lect-29 Kirchhoff’s Laws Kirchhoff’s Current Law (KCL) –sum of all currents entering a node is zero –sum of currents entering node is equal to sum of currents leaving node Kirchhoff’s Voltage Law (KVL) –sum of voltages around any loop in a circuit is zero

ECE201 Lect-210 KCL (Kirchhoff’s Current Law) The sum of currents entering the node is zero: Analogy: mass flow at pipe junction i 1 (t) i 2 (t)i 4 (t) i 5 (t) i 3 (t)

ECE201 Lect-211 Class Examples Learning Extension E2.3(b) Learning Extension E2.4 Learning Extension E2.5(a)

ECE201 Lect-212 KVL (Kirchhoff’s Voltage Law) The sum of voltages around a loop is zero: Analogy: pressure drop thru pipe loop v1(t)v1(t) + + – – v2(t)v2(t) v3(t)v3(t) +–+–

ECE201 Lect-213 KVL Polarity A loop is any closed path through a circuit in which no node is encountered more than once Voltage Polarity Convention –A voltage encountered + to - is positive –A voltage encountered - to + is negative

ECE201 Lect-214 Class Examples Learning Extension E2.6 –Use two different directions Learning Extension E2.7

ECE201 Lect-215 Electrical Analogies (Physical)