Review 2

# Review 2 - DC Circuits Chapter 19 (Giancoli) All sections...

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1 DC Circuits • Chapter 19 (Giancoli) • All sections CIRCUITS How to analyze DC circuits ? • Combinations of EMF ’s • Combinations of resistors • Combinations of capacitors • Combinations of resistors and capacitors Internal Resistance and Terminal Voltage The aging of a battery, due to the consumption or corrosion of its electrodes and the breakdown of its electrolyte, results in a reduction in its output or terminal voltage . These losses can be represented by an internal resistance . A real battery can be represented by The voltage between A and B is the terminal voltage of the battery, V AB , and r is the internal resistance of the battery. ε is the EMF of the battery. For an ideal battery, r = 0 and ε = V AB . ε r A B An external resistor with resistance R is connected to a real battery as shown. Power generated by the battery = ε I Power dissipated by the resistors = I 2 R + I 2 r ε I = I 2 R + I 2 r, ε = IR + Ir but IR = V AB ε = V AB + Ir V AB = ε -Ir V AB < ε ε R r AB In some cases, such as recharging a battery, V AB = ε + Ir ε = battery being charged r ε c = charging battery Power generated by the charging battery = ε c I Power received by the recharging battery and dissipated in the internal resistor = ε I + I 2 r ε c I= ε I + I 2 r so ε c = ε + Ir but ε c = V AB V AB = ε + Ir I Combination of EMFs 1. EMFs in series Example 1: Equivalent EMF: ε = 8V + 6V = 14V r = 2 + 3 = 5 14V 5 AC 2 3 ABC 8V 6V © Z. Altounian

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2 Combination of EMFs 1. EMFs in series Example 2: Equivalent EMF: ε = 8V - 6V = 2V r = 2 + 3 = 5 2V 5 AC 8V 2 3 (-)6V ABC Combination of EMFs 1. EMFs in series Example 3: Equivalent EMF: ε = - 8V + 6V = - 2V r = 2 + 3 = 5 2V 5 (-)8V 2 3 6V Rule : The algebraic sum of the individual EMFs and internal resistances of all the batteries connected in series gives the equivalent EMF and internal resistance of the combination. 2. EMFs in parallel 8V 2 AB 6V 3 No simple rule to find equivalent EMF and internal resistance. Need to learn more on circuit analysis. Combination of resistors 1. Resistors in series Neglect the resistance of the wires that make up the connections in the circuit. The same current flows through both resistors. Total potential difference V = V 1 + V 2 V = I 1 R 1 + I 2 R 2 V = I ( R 1 + R 2 ) V = IR eq V I R 1 R 2 V 1 V 2 I I The equivalent or total resistance is R eq = R 1 + R 2 The equivalent circuit is V R eq In general, for resistors connected in series: R eq = R 1 + R 2 + R 3 + ··· © Z. Altounian
3 1. Resistors in parallel R 1 and R 2 are connected to the same points A and B Potential difference across R 1 is equal to the potential difference across R 2 . V I R 1 R 2 I 1 I 2 I AB The battery is also connected to points A and B V 1 = V 2 = V The current from the battery I splits into two parts at the junction, point A .

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## This note was uploaded on 04/07/2008 for the course PHI 102 taught by Professor Altonian during the Winter '08 term at McGill.

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Review 2 - DC Circuits Chapter 19 (Giancoli) All sections...

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