Question

The voltage in a wall socket has been measured, andWall Blender found to be equal to Socket ig(t) s(t)-163cos(377[rad/s)o)IV]. V (t) A blender is connected to this wall socket, and the current in the blender is measured and found to be ¡B(1) 4.60cos(377[rad's]s-S)[A]. The diagram shows the voltage and current polarities in this connection.

a) Find the power absorbed by the blender at 0.
b) Find the power absorbed by the blender at t 4.3[ms].
c) Find the power absorbed by the blender at t-8.6[ms).
d) Find the energy absorbed by the blender over one cycle of the sinusoid.

Answer 1

To calculate the power absorbed by the blender, the product of voltage and current at specific times is used. For energy absorbed over a cycle, the average power is found first and then multiplied by the period of the cycle.

Step-by-step explanation:

The student is asking about calculating the power absorbed by a blender connected to an AC voltage source at different moments in time and also the energy absorbed over a complete cycle. To find the power absorbed by the blender, we use the formula P = IV, where P represents power, I is the current, and V is the voltage. Since the voltage and current both have a sinusoidal form, with voltage expressed as V(t) = 163 * cos(377t) and current as I(t) = 4.60 * cos(377t), the power at any instant can be found by multiplying these two expressions. To calculate energy over one cycle, we would integrate the power over the period of one cycle.

To find the power absorbed by the blender at specific times, substitute the values of t into both the voltage and current expressions and then apply the power formula. For example, at t = 0 ms, V(0) = 163 * cos(377*0) = 163 V and I(0) = 4.60 * cos(377*0) = 4.60 A, so P(0) = 163 V * 4.60 A = 749.8 W. This procedure would be repeated for other specific times, such as 4.3 ms and 8.6 ms.

For the energy absorbed over one cycle, we'd recognize that because the power wave is sinusoidal and the voltage and current are in phase, the average power over one cycle would be Pave = (V_peak)(I_peak)/2. Since we're dealing with a complete cycle, we can calculate energy using Energy = Pave * T, where T is the period of one cycle.