Question

Related rates question

Answer 1

what is the full question?

Answer 2

Here it is

Answer 3

Try posting a higher res image. It's hard to read, and zooming in doesn't do any favors.

Answer 4

sorry for my sloppiness. here is the question: The way that resistors are arranged in a circuit can affect the overall resistance of a circuit. In a series resistor arrangement, there is only one path for the current to flow from the battery (see diagram). As a result, the total resistance of the circuit is defined as Rs=R1+R2. In a praleel resistor arrangement there is two paths for the current to flow from the battery. As a result the total resistance of the circuit is defined as \[\frac{ 1 }{ Rp } = \frac{ 1 }{ R1 } + \frac{ 1 }{ R2 }\]. Note: resistance of a resistor is measured in ohms.

A student discovers that when R1=4 ohms, its resistance is increasing at a rate of 0.1ohms/s. A similar study also reveals that when R2= 2 ohms, its respective resistance is decreasing at a rate of 0.05 ohms/s. Assume that these resistances and their respective rates of changes are the same regardless of the circuit being used.

a) Find the rate of change of the total resistance of a series resistors arrangement using the above information
b) Find the rate of change of the total resistance of a parallel resistors arrangement using the above information hint: \[\frac{ 1 }{ Rp } = \frac{ 1 }{ R1 } + \frac{ 1 }{ R2 }\] is equivalent to (Rp)^-1=(R1)^-1 + (R2)^-1
c) Which resistor arrangement has the greatest rate of change in totlal resistance with respect to time?

(the pic i posted has the diagram)

Answer 5

a) Rs=R1+R2
dRs=dR1+dR2

b) (1/Rp)=(1/R1) + (1/R2)
(-1/Rp^2)dRp=(-1/R1^2)dR1 + (-1/R2^2)dR2

c) dRp/ dRs = ?

these differentials give you an awful lot of flexibility. you can stuff a dt underneath and imagine that you are modelling it wrt time, which you are.