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Karo-lina-s [1.5K]
2 years ago
10

Suppose the voltage in an electrical circuit varies with time according to the formula V(t) = 40 sin(t) for t in the interval [0

,].
The numerical value of the mean voltage in the circuit is
Mathematics
1 answer:
grigory [225]2 years ago
7 0

The numerical value of the mean voltage is 25.47 V

To find the numerical value of the mean voltage, V of V(t) = 40 sin(t), we integrate V(t) with respect to t over the interval [0.π]

So,

V = \frac{1}{\pi } \int\limits^\pi _0 {V(t)} \, dt \\V = \frac{1}{\pi } \int\limits^\pi _0 {40sint} \, dt \\V = \frac{1}{\pi } [-40cost]_{0}{\pi }  \\V = \frac{1}{\pi } -[40cos\pi  - 40cos0]\\\\V = \frac{1}{\pi } (-[40 X (-1) - 40 X 1})\\V = -\frac{1}{\pi } [-40 - 40]\\V = \frac{80}{\pi } \\V = 25.465 V

V ≅ 25.47 V

So, the numerical value of the mean voltage is 25.47 V

Learn more about mean volatage here:

brainly.com/question/17928028

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