A circuit contains infinitely many resistors connected in parallel. Each successive resistor has a resistance of double that of the previous one.
What is the equivalent resistance of the resistors in this circuit?
Infinite resistors help Watch
- Thread Starter
- 30-09-2016 19:51
- 01-10-2016 19:45
I think that the answer is Half an ohm. the first resistor has resistance on 1 ohm. The rest forms an infinite geometric series that converges.
using the equation (1-r)/r to give the sum of the series
1/2+1/4+1/8,... (1/2)^n r=1/2 because r is the multiplication factor 1/2 * r = 1/2 and 1/4 * r = 1/8 sp r = 1/2. you could thing of it as if you are doubling each time your reciprocal is halving each time. (1-0.5)/).5 = 1 ohm, the reciprocal of this is 1. so we have one ohm but there still that pesky 1/1 ohm resistor at the start. i think that means 1/RT = 2 so RT = 0.5
weird question really requires a level maths not taught in physics.