Download Lecture 5: Series and Parallel Resistors in Electrical Circuits and more Slides Microelectronic Circuits in PDF only on Docsity! 1 Lecture 5, Slide 1EECS40, Fall 2003 Prof. King Lecture #5 OUTLINE • Resistors in series – equivalent resistance – voltage-divider circuit – measuring current • Resistors in parallel – equivalent resistance – current-divider circuit – measuring voltage • Circuit w/ dependent source example Reading Chapter 3.1-3.5 Lecture 5, Slide 2EECS40, Fall 2003 Prof. King Clarification of Terms • If p > 0, then the circuit element is absorbing electric power from the rest of the circuit. (Power is delivered to the element.) – For a resistor, energy is dissipated in the form of heat – For a source, energy is stored • If p < 0, then the circuit element is supplying electric power to the rest of the circuit. (The element is said to be developing power or generating power; this power is delivered to the rest of the circuit.) + v _ i 2 Lecture 5, Slide 3EECS40, Fall 2003 Prof. King Consider a circuit with multiple resistors connected in series. Find their “equivalent resistance”. • KCL tells us that the same current (I) flows through every resistor • KVL tells us Equivalent resistance of resistors in series is the sum R2 R1 VSS I R3 R4 − + Resistors in Series Lecture 5, Slide 4EECS40, Fall 2003 Prof. King I = VSS / (R1 + R2 + R3 + R4) Voltage Divider + – V1 + – V3 R2 R1 VSS I R3 R4 − + 5 Lecture 5, Slide 9EECS40, Fall 2003 Prof. King What single resistance Req is equivalent to three resistors in parallel? + − V I V + − I R3R2R1 Req eq≡ General Formula for Parallel Resistors Equivalent conductance of resistors in parallel is the sum Lecture 5, Slide 10EECS40, Fall 2003 Prof. King Vx = I1 R1 = ISS Req Current Divider R2R1ISS I2I1 x 6 Lecture 5, Slide 11EECS40, Fall 2003 Prof. King R2R1 I I2I1 I3 R3 + − V + + = 321 R 1 R 1 R 1 IV ++ == 321 3 3 3 1/R1/R1/R 1/RI R VI Generalized Current Divider Formula Consider a current divider circuit with >2 resistors in parallel: Lecture 5, Slide 12EECS40, Fall 2003 Prof. King To measure the voltage drop across an element in a real circuit, insert a voltmeter (digital multimeter in voltage mode) in parallel with the element. Voltmeters are characterized by their “voltmeter input resistance” (Rin). Ideally, this should be very high (typical value 10 MΩ) Ideal Voltmeter Rin Measuring Voltage 7 Lecture 5, Slide 13EECS40, Fall 2003 Prof. King + = 21 2 SS2 RR RVV + =′ 1in2 in2 SS2 RR||R R||RVV Example: V1VK900R ,K100R ,V10V 212SS =⇒=== VSS R1 R2 If ,V991.0V ,M10R 2in =′= VSS R1 R2 Rin Effect of Voltmeter undisturbed circuit circuit with voltmeter inserted _+ _+ + – V2 + – V2′ Lecture 5, Slide 14EECS40, Fall 2003 Prof. King Find i2, i1 and io Circuit w/ Dependent Source Example
