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Understanding Kirchoff's First Law in Electrical Current Calculation

Learn how to apply Kirchoff's First Law to calculate drift velocity in electrical currents and predict insulator number densities. Practice with sample problems involving copper, brass, and silver wires.

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Understanding Kirchoff's First Law in Electrical Current Calculation

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  1. From last lesson we found… VOL = distance x Area = speed x time x Area # ELECTRONS = charge/charge of 1 electron = current x time / e NUMBER DENSITY, n = # electrons/vol n = (I x t) n = I/evA e x v x t x A nAve = I

  2. The big question: What did Kirchoff say? Why are we learning this? Supermax (super maximum security) prisons e.g. Alcatraz

  3. Learning Objective: To evaluate Kirchoff’s first law The big question: What does Kirchoffsay? A – B – C – D -

  4. Calculate velocity A copper wire has cross-sectional area 3.0 mm2 and current 5.0A. Copper’s number density is 6.0x1028m-3. A brass wire has cross-sectional area 6.0mm2 and current 9.0A. Assume Brass’s number density is 9.0x1028 m-3. A brass wire has radius ½ that of the previous question, with the same current.

  5. On a whiteboard: (b) A silver wire has cross-sectional area 3.0 mm2 and current 2.0A. Copper’s number density is 4.0x1028 m-3. (A) If the radius was ¼ as small, then the number of electrons will be what factor smaller?

  6. Learning Objective: To combine knowledge on density and electricity to calculate velocity The big question: How do we combine density with velocity? A – Predict insulator number densities B – Analyse how number density changes drift velocity C – Create a formula for drift velocity and Current D – Calculate drift velocity

  7. Calculate mean drift velocity: A copper wire has cross-sectional area 4.0 mm2 and current 5.0A. Copper’s number density is 8.0x1028 m-3. A brass wire has cross-sectional area 6.0mm2 and current 15.0A. Assume Brass’s number density is 9.0x1028 m-3. (C) Using letters n for number density, I for current, e for charge of 1 electron and A for cross-sectional area, write an expression for v

  8. What do they do? A – Predict insulator number densities, using your expression from C and B B – Analyse how number density (n) changes drift velocity. Keep all other numbers the same and change n up and down, to see the effect on velocity C – Create a formula for drift velocity, v and rearrange it for current, I

  9. Current, I = nA/veve/nA n/vAenAve

  10. If the wire had a high number density V is velocity v would increase v would stay the same v would decrease

  11. If the wire was an insulator number density number density would increase would decrease number density would stay same

  12. Learning Objective: To combine knowledge on density and electricity to calculate velocity The big question: How do we combine density with velocity? A – Predict insulator number densities B – Analyse how number density changes drift velocity C – Create a formula for drift velocity and Current D – Calculate drift velocity

  13. Learning Objective: To combine knowledge on density and electricity to calculate velocity The big question: How do we combine density with velocity? A – Predict insulator number densities B – Analyse how number density changes drift velocity C – Create a formula for drift velocity and Current D – Calculate drift velocity

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