Question

The voltage v in a circuit is given by the equation v(t) = 3sin(100πt), t ≥ 0 where t is measured in seconds.

(a) Write down the maximum and minimum value of v.

Answer 1

The maximum value of voltage in the given AC circuit is 3 V, and the minimum value is -3 V, as determined from the amplitude of the sine function in the voltage equation.

Step-by-step explanation:

The question relates to the maximum and minimum values of voltage in an AC circuit, which can be identified directly from the equation of the voltage given by v(t) = 3sin(100πt). In a sine function, the maximum value is equal to the amplitude, and since the amplitude is 3 in this case, the maximum voltage is 3 V. Similarly, the minimum value is the negative of the amplitude, which gives us -3 V for the minimum voltage. Therefore, the voltage in the circuit ranges between -3 V and 3 V over time. This conclusion is derived by analyzing the given sinusoidal function for voltage without the need for a phase constant in this context.