Recent content by iainfs

Ah, OK then. I'm from the UK and we do things in a slight different order! Do you know the small angle approximations? \sin\theta \approx \tan\theta \approx \theta for small \theta in radians.

Try expanding numerator and denominator as Maclaurin series.

Thank you! Knew there would be a more elegant way.

Homework Statement Prove \sum^{2n}_{r=1} r^3 = n^2(2n+1)^2 by mathematical induction. My proof is below but it is rather long winded. Is there a quicker way of doing the algebraic manipulation? Preferably one that forgoes the polynomial division and multiplying out all the brackets! The...

I had another attempt. Still no joy unfortunately. I = \frac{V_i}{R_1+R_2} I^2 = \frac{V_i^2}{(R_1+R_2)^2} P_{R_2} = I^2R = \frac{V_i^2 \cdot R_2}{(R_1+R_2)^2} Alternatively, using P = VI: I = \frac{V_i}{R_1+R_2} V_o = \frac{V_i \cdot R_2}{R_1+R_2} P = V_oI = \frac{V_i^2 \cdot...

I'm sorry, I'm struggling with that one. Do you mean power as would be given by P = I^2 x R? Another possible point of confusion I have noticed is that a common type of potential divider has R1 + R2 = constant = the total resistance on the potentiometer. Mine uses a fixed resistor for R1; R2...

Thanks for your reply. Yes, that would make sense. I think I have been misled as to the benefits of R1 = R2. For pure sensitivity (volts/ohm), a very large pot is best. What, then, are the benefits of R1 = R2? Many thanks.

Hi folks, Homework Statement We have a voltage divider (more specifically, a resistive divider), with V_i volts input and resistors R_1 and R_2 in series. The output voltage, V_o, is measured over R_2. R_1 is a fixed ohmic resistor; R_2 is a potentiometer. I'm looking for an algebraic...