Assignment math

12. The voltage V (in V, volts) across a circuit is given by Ohm’s Law: V = IR, where I is the current (in A, amps) flowing through the circuit and R is the resistance (in Ω, ohms). If we place two resistors, with resistance R1 and R2, in series, then their combined resistance R is given by

R = R1 + R2.

Suppose the current is 1 A and increasing at 0.1 A/sec and R1 is 2 Ω and decreasing at 0.3 Ω/sec, while R2 is 3 Ω and increasing at 0.2 Ω/sec.

Make sure to include units!

Make sure to include units!

9

(a) Draw a diagram to indicate the dependencies among all the variables.

(b) Determine the value of the combined resistance R.

(c) Compute ∂R/∂R 1and ∂R/∂R 2for R 1= 2 Ω and R 2= 3 Ω. Make sure to include units!

(d) Calculate dV/dt, the rate at which the voltage is changing with respect to time.