Batch 2 - Class 66 - Electric Circuits

• Solve YEAR * 12 = MONTH by replacing each letter by a unique digit 1..9. H > T

  Answer:  6129 * 12 = 73548
• I have a 24L of water in a jar. Can you divide into 3 equal parts using only a 13L, a 5L and an 11 liter Jar and of course 24L jar.

  Answer

  24 13 11 5

  ----------

  24 0 0 0 

  11 13 0 0 

  6 13 0 5

  6 2 11 5

  8 0 11 5

  8 5 11 0

  8 13 3 0

  8 8 3 5

  8 8 8 0

• River Dam Analogy

  Consider a river that consists of a trench dug connecting two lakes of equal heights. Will water flow in either direction?What if the water height was same but one lake was deeper?What if one lake was higher than the other?What if we widen one of the trenches without changing its height?

• What if we increased the height difference between the two lakes? Will the flow increase or decrease?
• Can we try to write the flow as function of the height difference? Lets call it push
• What will happen if the trench had a lot of rubble in it?
• What if the trench was made really smooth?
• Can we try to write the flow as a function of the resistance in the trench?
• Arrive at the  relationship flow=push/resistance
• Lightning

  Why does lightning happen? (Difference in charge - accumulated electrons)What happens in lightning? (charge flows trying to equalize the electric potential)Analogy to dam scenario, where water flows to try and equalize heightJust like water needs a trench to flow, electrons need a conductor to flow - "closed circuits"What do you think would happen to the flow if there was a lot of difference in charge?What do you think would happen to the flow if the wire the conductor wasn't as good?Can we try to write the flow (current) as a function of difference in charge (potential difference) and resistance?Voila! We just discovered Ohm's Law!Units of potential difference, current and resistance are volt, ampere and ohms, such that 1 V = 1 A & 1 Ohm
• Exercise - Suppose a floor lamp with resistance of 5 Ohm required a current of 70 A to properly function. What is the potential difference that must be applied?

  Answer: 350 V
• Resistors in Series

  If there are three resistors in series to a battery, what is the total resistance and current?Lets think back in terms of trenches - if there are three trenches along the way, what can we say about the flow through each?Overall, should there be more flow than one trench or less?What would be the potential difference across each trenchWhat is the sum of these potential differences? (say similar to sum of height differences?)Now can we arrive at a way to connect individual resistance to overall resistance?Same concept applies to circuits - current through each resistor must be the same, and hence R = R1 + R2 + R3Note that voltage across each resistor is different, and sum to those is the total voltage differenceThink about it as an electron moving, gaining kinetic energy due to voltage difference, and then losing some of it going through the resistor - In a full cycle, it must gain as much as it lostWhat will happen if you connect many electric devices in series?Will each get enough current?What if one device fails?Have you observed this in diwali/christmas lights?
• Resistors in Parallel

  If there are three resistors in parallel to a battery, what is the total resistance and current?Lets think back in terms of trenches - if there are three trenches in parallel, what can we say about the flow through each?Overall, should there be more flow than one trench or less?What would be the potential difference across each trench, and flow through them?What is the sum of these flows?Now can we arrive at a way to connect individual resistance to overall resistance?Same concept applies to circuits - voltage across each resistor must be the same, and hence 1/R = 1/R1 + 1/R2 + 1/R3Note that current through each resistor is different, and sum to those is the total currentWhat will happen if you connect many electric devices in parallel?Will each get enough current?What if one device fails?Household appliances are connected in parallel for this reason
• Exercise: Find the effective resistance across points A and B

• Infinite Ladder of Resistors - Calculate the effective resistance of this circuit 

• Answer: 2
• (Geoffrey - 149) 15 Turks and 15 Christians were aboard a ship caught in a severe storm. The captain decided to throw half of the passengers overboard. To be fair, he asked everyone to stand in the circle, and he would throw every 13th person in the circle. A clever Christian pointed out to his fellow man a way to stand so that only all the turks would get thrown out. Can you find that arrangement?

  

• Infinite Circles of Resistors  - In the circuit below colored lines are 1 Ohm resistors, and black lines are connecting wires. The first (innermost) circle has 8 resistors, the next 16, the next 32 and so on infinitely. What is the total resistance of the circuit?