1. DC Circuit Analysis HRW P639>

2. Circuit Symbols • Resistor • Voltage source (battery) • Switch • Wire (Conductor)

3. What is a circuit? • A basic circuit comprises: • Voltage source (ex. battery) • Load (ex. Resistors) • Conductor (ex. Wires) • Control (ex. Switch)

4. DC Circuit Analysis • DC Circuits are analyzed in 3 models • Series resistors • Parallel resistors • Combination resistors • Circuit Analysis investigates: • Equivalent resistance • Circuit current in/out battery • Voltage drop across components • Currentthrough components

5. DC Circuit Analysis - Series • Components are connected “nose-tail” or inline • There is only one path for the circuit current (I) to flow.

6. Examples of series circuits

7. DC Circuit Analysis – Series • Equivalent (or total) resistance • RT = R1 + R2 + R3 • Current is the same through all components = circuit current (I) • Voltage drop across each resistor (n) • Vn = I*Rn • Sum of voltage drops = battery voltage

8. DC Circuit Analysis – Series Practice • Analyze the series circuit by calculating: • Equivalent resistance RT • Circuit current (I) flowing into/out of the battery • Voltage drop across the 3, 4 and 5 ohm resistor

9. DC Circuit Analysis - Parallel • Components are connected “side by side” • There are multiple paths for the current to flow, splitting into branch currents through R1, R2 and R3, according to their resistive values. • The circuit current (I) flows into/out of the battery.

10. Examples of parallel circuits

11. DC Circuit Analysis – Parallel • Equivalent resistance • 1/RT = 1/R1 + 1/R2 + 1/R3 • Voltage is the same across all n resistors (V) • Current in each resistor (In) • In = V/Rn

12. DC Circuit Analysis – Parallel Practice • Analyze a parallel circuit by finding: • Equivalent resistance (RT) • Circuit current (I) • Current (In) through each of the resistors Rn • I1 through R1 • I2 through R2 • I3 through R3

13. DC Circuit Analysis – Combo • Resistors are connected in both series (R3) and parallel (R1, R2) methods • Analyze by starting to simplify from the inside-out: • Simplify R1 and R2 > R12 • Add result (R12) to R3 for total circuit resistance (Rtot) • Calculate circuit current • I = V/Rtot • Calculate currents through selected resistances

14. Parallel part of combo • Consider current (I) • Passes through R3 in series with battery • Splits so that larger part goes through the low value resistor (Rlow) , and smaller part goes through high value (Rhigh) resistor

15. DC Circuit Analysis – Combo Practice • Given V = 12V, R1, R2 and R3 = 1, 2, 3 ohm respectively, calculate: • Equiv resistance (RT) • Circuit current (I) • Current through R2 (I2) • See next slide

16. Combo Shortcut for current • R1 and R2 are in parallel, so the voltage drop across each resistor is the same. • Shortcut for calculating In when there are 2 resistors (Rlow and Rhigh) in parallel: • Ilow = (Rhigh/(Rlow + Rhigh) * circuit current (I) • Ihigh = (Rlow/(Rlow + Rhigh) * circuit current (I) • We are simply apportioning the current according to the resistance • Higher resistance = lower current (and v.v) Ilow = current through Rlow & Ihigh = current through Rhigh