Question

When voltages V1=30sin(100πt) and V2=40cos(100πt) are applied to the same circuit, the resulting voltage V is equal to their sum.

(a) GraphV=V1+V2 in the viewing rectangle [0,0.05,0.01] by [−80,80,40].

Answer 1

The graph depicts the resulting voltage V = V₁+ V₂, which is a combination of a sine wave and a cosine wave, fluctuating between -80 and 80 volts over time. The graph can be seen on the attachment.

Step-by-step explanation:

The graph represents the resulting voltage V when two voltages, V1=30sin(100πt) and V2=40cos(100πt), are combined in a circuit. At different points in time (horizontal axis), the combined voltage V (vertical axis) is plotted.

Since V is the sum of V₁ and V₂, its waveform is a combination of a sine wave and a cosine wave. The amplitude of the resulting wave varies between -80 and 80 volts due to the sum of the individual amplitudes. The frequency of the resulting wave remains the same as the individual waves, as they have the same angular frequency of (100π) radians per second.

The resulting wave's shape is a combination of both sinusoidal and cosine patterns, creating a waveform that fluctuates smoothly between positive and negative values. The constructive and destructive interference between the sine and cosine functions results in a complex but periodic pattern for the combined voltage V over time.