Question

Consider the RC circuit shown in Figure. The relationship between the input x(t) and the output y dy(t) is given in that form, + ay(t) = bx (t) +c dt where R=1ohm, and C=5Farad. R + 1 us(t) i(t) volt) If y(t)= vs(t) and y(t)= vc(t) what is the value of b?

Answer 1

In an RC circuit with R = 1 ohm and C = 5 farads, the value of the variable 'b' from the differential equation relates to the resistance, which implies that b = 1.

Step-by-step explanation:

The student has asked about the value of variable b in the differential equation + ay(t) = bx(t) + c dy(t)/dt for a given RC circuit. This equation relates the input x(t) to the output y(t) in terms of the resistor R and the capacitor C. Given that R = 1 ohm and C = 5 farads, and considering the nature of an RC circuit, the value of b is typically related to the resistance in the circuit. Because the relationship between voltage and current in an RC circuit when being charged is governed by V = emf(1 - e-t/τ), where τ = RC, we can reason that b corresponds to the inverse of the resistance R since the current i(t) is related to the voltage x(t) by i(t) = x(t)/R. Given R = 1 ohm, it would imply that b = 1.