Understanding Ohm's Law & Power Dissipation in DC Circuits, Study notes of Law

Download Understanding Ohm's Law & Power Dissipation in DC Circuits and more Study notes Law in PDF only on Docsity! Review of DC Circuit Analysis EAS 199A Notes EAS 199A: DC Circuit Summary Overview 1. Ohm’s Law 2. Power dissipation 3. Resisters in series 4. Resistors in parallel EAS 199A: DC Circuit Summary page 1 Ohm’s Law (1) V = IR where V = voltage drop across the resistor (V) I = current through the resistor (A) R = resistance (Ω) V I R EAS 199A: DC Circuit Summary page 2 Ohm’s Law (2) Complex arrangements of resistors can be reduced to an equivalent resistance, Req, and then Ohm’s law can be applied to the equivalent circuit. R2 R3 R4 R5 R1 Vs Vs I Req I Req = R1 + 1 1 R2+R3 + 1 R4 + R5 Vs = IReq EAS 199A: DC Circuit Summary page 3 Resistors in Series on a Breadboard Sockets in a column are not connected Sockets in a row are connected Breadboard Schematic of breadboard Conductors along rows of breadboard EAS 199A: DC Circuit Summary page 8 Resistors in Parallel R2 VAB R1 ReqIA I I1 I2 IB BA VAB 1 Req = 1 R1 + 1 R2 Kirchoff’s voltage law tells us that the voltages across the resistors is the same V1 = V2 = VAB Kirchoff’s current law tells us that the current through the resistors adds: I = I1 + I2 EAS 199A: DC Circuit Summary page 9 Resistors in Parallel on a Breadboard Sockets in a column are not connected Breadboard Schematic of breadboard Sockets in a row are connected Conductors along rows of breadboard EAS 199A: DC Circuit Summary page 10 Example: Power dissipation for one resistor in a circuit (1) What power is dissipated by R5 in the circuit to the right? What is the total power dissipation of the circuit? Use the following system parameters. Vs = 10V R1 = R4 = 470Ω R2 = R3 = R5 = 330Ω R2 R3 R4 R5 R1 Vs I The power is P5 = V5I5, but neither V5 nor I5 is known. Use the alterative formula P5 = I2 5R5. Since R5 is known, the first step is to determine the current I5. Note that the current through R5 is the same as the total current leaving the battery, i.e., I5 = I. EAS 199A: DC Circuit Summary page 11 Example: Power dissipation for one resistor in a circuit (2) Solution Step 1: Replace the resistor network with a single equivalent resistor. R2 R3 R4 R5 R1 Vs Vs I Req I Req = R1 + 1 1 R2+R3 + 1 R4 + R5 Vs = IReq EAS 199A: DC Circuit Summary page 12 Example: Power dissipation for one resistor in a circuit (3) Solution Step 2: Substitute the known values to compute Req. Req = R1 + 1 1 R2+R3 + 1 R4 + R5 = 470Ω + 1 1 330+330Ω + 1 470Ω + 330Ω = 1074.5Ω Solution Step 3: Apply Ohm’s law to the equivalent circuit to compute the total current, I. Vs = IReq =⇒ I = Vs Req = 10V 1074.5Ω = 0.00931A EAS 199A: DC Circuit Summary page 13