Question

A non-ideal AC voltage source, vs has an open circuit terminal voltage amplitude of a and an internal resistance Rs. Given that: a = 0.6v, A = 6v and Rs = 49kΩ,

find the value of R required so that v₀ has an amplitude of A.

Answer 1

The value of resistor R that is required for v0 to have an amplitude of A in this non-ideal AC circuit is 49kΩ, calculated using the voltage divider rule and the given values of a, A, and Rs.

Step-by-step explanation:

To find the value of resistance R required so that v0 has an amplitude of A, we must consider the voltage divider rule in an electrical circuit. The open-circuit terminal voltage amplitude is a = 0.6V when no load is connected, and the source has an internal resistance Rs. When a load resistor R is connected, the amplitude of the voltage across the load resistor (v0) will be less than a because some voltage will be dropped across Rs.

The voltage across the load resistor can be calculated using the formula v0 = a * (R / (R + Rs)). To find R, we rearrange the formula to R = (v0 / a - 1) * Rs. Given that a = 0.6V, A = 6V (the desired amplitude for v0), and Rs = 49kΩ, we can substitute these values into the formula.

Thus, R = (6 / 0.6 - 1) * 49kΩ = (10 - 1) * 49kΩ = 49kΩ.

The required value of R for v0 to have an amplitude of A is 49kΩ.

Answer 2

In Physics, to determine the required resistance R that will give an amplitude of A across a non-ideal AC voltage source, we use the voltage divider rule and Ohm's law. However, given the provided values, it is not possible to achieve an amplitude of 6V across R because the open-circuit amplitude is only 0.6V.

Step-by-step explanation:

The subject of the question is Physics, specifically dealing with AC circuits and Ohm's law. The open circuit terminal voltage amplitude a of the non-ideal AC voltage source is given as 0.6V, with an internal resistance Rs of 49kΩ. We want to determine the external resistance R needed so that the voltage v0 across it has an amplitude of A when connected to this source.

When a resistor R is connected across the non-ideal AC voltage source, the total voltage across R is divided according to the voltage divider rule. This is illustrated by the equation VR = (R / (R + Rs)) × a, where VR is the desired amplitude across R. We can solve for R by rearranging the equation as R = (A × Rs) / (a - A) and substituting the given values.

Given a = 0.6V, A = 6V, and Rs = 49kΩ, we plug these into the equation to find R. Hence, R = (6V × 49kΩ) / (0.6V - 6V). Calculating this we find that R is approximately -8.17kΩ, which is not physically meaningful. This result indicates an error as resistance cannot be negative, implying that with the given values, it's not possible to achieve an amplitude of 6V across R since the open-circuit amplitude is only 0.6V.