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Download Lecture #12 03/01/05
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Announcements • Quiz II March 3rd – Lectures 6-10 – Chapters 25,26, and 27 through Tuesday 02/22 – Slightly shorter: 10 MC and 3 SA • There is a midsemester survey on webassign • Most of you did not give an example on today’s reading quiz. Full Credit now, but not if it shows up elsewhere! • Office Hrs: Today – 2-3pm Batteries •An ideal battery creates a voltage difference between the two sides E P I V E2 P R – + R If we can neglect the internal resistance in the battery, the current in this simple circuit is just: V I R R Power Consumed by a Resistor V=E + E – R I = E/R P I V V=0 dU d dQ P QV V I V dt dt dt 2 V 2 P RI R Series Resistors •Two or more resistors connected together can be treated as one giant resistor •For resistors in series, the current is the same through both of them R1 R2 V1 = R1 I V2 = R2 I V = V1+ V2 = R1 I + R2 I = (R1 + R2 )I R = R1 + R2 Series Circuits R1 R2 Resistors V1 = R1 I R = R1 + R2 V2 = R2 I Current is the same through each resistor Capacitors: C1 C2 C3 1 1 1 1 C C1 C2 C3 Charges are the same on each capacitor Real Batteries •An real battery has an internal resistance E How does this affect the current? Ir IR 0 I Rr – r + R real battery Parallel Resistors •Two or more resistors connected together can be treated as one giant resistor •For resistors in parallel, the voltage is the same across both of them V = R2 I2 R1 R2 V = R1 I1 1 1 1 R R1 R2 1 1 V V V I I1 I 2 R1 R2 R1 R2 Parallel Circuits Voltages are the same across each element Resistors 1 1 1 R R1 R2 R1 Capacitors C1 Same Voltages C2 C3 C C1 C2 C3 What is the combined resistance of the mess at right? A) 1.5 k B) 12 k C) 14 k D) 21 k 9 k 3 k 3 k 6 k 3 k 2 k R R1 R2 3 3 6 1 1 1 1 1 1 R R1 R2 3 6 2 R R1 R2 R3 3 9 2 14 3 k Kirchoff’s Rules •The total current flowing into a point must equal the total current flowing out of a point [conservation of charge] •The total voltage change around a loop must total zero I2 I3 V1 V2 – + I1 I3=I2+I1 V3 V1 + V2 + V3 = 0 Using Kirchoff’s Rules •Draw a (circuit) diagram and label everything known or unknown! •To every series of components, assign a direction to the current I (don’t worry if you get it wrong, the result will be correct just negative) •You must be consistent however after you assign a direction! •Write down conservation of charge at each vertex •Write down one equation for each loop •In an emf source, going – to + gives a positive V, + to - is a negative V •Solve all equations You might end up with many equations, but I trust that you can solve simultaneous equations. A Multiloop Circuit I1 + I3 = I2 1.5 – 3I2 = 0 9 – 5I1 – 3I2 = 0 I2 = 1.5/3 = 0.5 A I1 = (9 – 3I2)/5 = 1.5 A I3 = I2 – I1 = 0.5 – 1.5 = – 1 A I1 – + 9V 5 I2 3 1.5 V – + I3 What Whatisisthe thevoltage conservation loop rule of you current get applied law associated to the upper with loop? the junction on the right? A) A) 9I1++5II21 =+ I3I 32=0 B) B) 9I+1 +5II13 –=3I I22 = 0 C) C) 9I–2 +5II13+=3I I12 = 0 D) D) 9I1–+5II21 + – 3I I3 2==00 A Multiloop Circuit •There is one more loop in the problem. 9 – 5I1 -1.5 = 0 I1 = (9 – 1.5)/5 = 1.5 A I1 – + 9V 5 I2 3 1.5 V – + I3 •We only had one resistor and so only had to consider one current. This can simplify problems! Odd Circuit What is the current through the resistor? A) 3.6 A B) 1.8A C) 90 A D) 0 A – + 9V 5 9V – +