Question

Given the following voltage and current:

i(t)=5sin(377t−76º)A
u(t)=10cos(377t+73º)V

Determine the phase relationship between i(t) and u(t).

Answer 1

The voltage u(t) leads the current i(t) by 239 degrees in their phase relationship.

Step-by-step explanation:

To determine the phase relationship between the current i(t) and voltage u(t), we first express both functions in the sine form. The current is given by i(t) = 5sin(377t−76º) A and the voltage is given by u(t) = 10cos(377t+73º) V. To compare them, we convert the voltage expression to sine using the identity sin(x) = cos(x - 90º).

Therefore, u(t) becomes: 10sin(377t+73º+90º) which simplifies to 10sin(377t+163º).

The phase angle of the current i(t) is -76º, and the phase angle of the voltage u(t) after converting to sine is +163º. The phase difference φ between the voltage and current is calculated by subtracting the phase of the current from the phase of the voltage: φ = 163º - (-76º) = 239º. This means that the voltage u(t) leads the current i(t) by 239º.