The voltage across the terminals of an ac power supply varies with time according to V=V0cos(t). The voltage amplitude is V0 = 41.0V . A. What is the root-mean-square potential difference Vrms?
B. What is the average potential difference Vav between the two terminals of the power supply?

A. The root-mean-square potential difference () is equal to 28.99 Volts.

B. For this voltage with a sinusoidal waveform (sine wave), the average potential difference () between the two terminals of the power supply is equal to zero (0).

Given the following data:

The voltage across the terminals of an alternating current (AC) power supply varies directly with time according to the equation:

A. To find the root-mean-square potential difference ():

Mathematically, root-mean-square for voltage in an alternating current (AC) power supply (circuit) is given by the formula:

Substituting the given parameter into the formula, we have;

B. To find the average potential difference () between the two terminals of the power supply:

For this voltage with a sinusoidal waveform (sine wave), the average potential difference () between the two terminals of the power supply is equal to zero (0).

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A) V_rms = 29 V

B) Vav = 0 V

Explanation:

A) We are told that;

V = V_o cos ωt

voltage amplitude; V = V_o = 41.0V

Now, the formula for the root-mean-square potential difference Vrms is given as;

V_rms = V/√2

Thus plugging in relevant values, we have;

V_rms = 41/√2

V_rms = 29 V

B) Due to the fact that the voltage is sinusoidal from the given V = V_o cos ωt, we can say that the average potential difference Vav between the two terminals of the power supply would be zero.

Thus; Vav = 0 V