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DC Circuit Analysis HRW P639>

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Circuit Symbols Resistor Voltage source (battery) Switch Wire (Conductor)

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

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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 Current through components

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

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Examples of series circuits

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DC Circuit Analysis – Series Equivalent (or total) resistance R T = R 1 + R 2 + R 3 Current is the same through all components = circuit current (I) Voltage drop across each resistor (n) V n = I*R n Sum of voltage drops = battery voltage

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

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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.

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Examples of parallel circuits

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DC Circuit Analysis – Parallel Equivalent resistance 1/R T = 1/R 1 + 1/R 2 + 1/R 3 Voltage is the same across all n resistors (V) Current in each resistor (I n ) I n = V/R n

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DC Circuit Analysis – Parallel Practice Analyze a parallel circuit by finding: Equivalent resistance (R T ) Circuit current (I) Current (I n ) through each of the resistors R n I 1 through R 1 I 2 through R 2 I 3 through R 3

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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 > R 12 Add result (R 12 ) to R3 for total circuit resistance (R tot ) Calculate circuit current I = V/R tot Calculate currents through selected resistances

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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 (R low ), and smaller part goes through high value (R high ) resistor

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

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Combo Shortcut for current R 1 and R 2 are in parallel, so the voltage drop across each resistor is the same. Shortcut for calculating I n when there are 2 resistors (R low and R high ) in parallel: I low = (R high /(R low + R high ) * circuit current (I) I high = (R low /(R low + R high ) * circuit current (I) We are simply apportioning the current according to the resistance Higher resistance = lower current (and v.v) I low = current through R low & I high = current through R high

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