Question

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?

Answer 1

Answer:

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

Answer 2

A. The root-mean-square potential difference ($V_{rms}$) is equal to 28.99 Volts.

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

Given the following data:

• Voltage amplitude = 41.0 Volts.

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

$V_0 = V_0cos(t)$

A. To find the root-mean-square potential difference ($V_{rms}$):

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

$V_{rms} = \frac{V}{\sqrt{2} }$

Substituting the given parameter into the formula, we have;

$V_{rms} = \frac{41}{\sqrt{2} }\\\\V_{rms} = \frac{41}{1.4142 }\\\\V_{rms} = 28.99\; Volts$

B. To find the average potential difference ($V_{ave}$) between the two terminals of the power supply:

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

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