Question

Find the power delivered to the element in Example 1.5 at t = 5 ms if
the current remains the same but the voltage is: (a) v = 2i V, (b) v =
10 + 5
t
0
i dt

V.

Answer 1

Answer:

(i) Power delivered is 17 watt

(ii) Power delivered is 29.7 watt

Step-by-step explanation:

Given as :

At time t = 5 ms

The current through element = i  Amp

(i) voltage = 2 i  volt

∵ The current in an element = i = 5 cos 60πt

So, v(t) = 2 i(t)

Or, v(t) = 2 ( 5 cos 60πt)

Or, v(t) = 10 cos 60πt

at t = 5 ms

v(5 ms) = 10 × cos 60π(5 ms)

i.e v(5 ms) = 10 × cos 0.3π

∴ voltage at t = 5 sec is 5.8 volt

So, power = p = v × i

Or, p = 5.8 × 5 cos 60πt

Or, p = 29 cos 0.3π

i.e p = 17 watt

Hence, Power delivered is 17 watt

(ii) v = 10 + 5 $\int_{0}^{t}$ i dt

Or, v = 10 + 5 $\int_{0}^{0.005}5 cos60\pi t dt$

Or, v = 10 + 25 × $\dfrac{1}{60\pi }$ [ sin 60π × 0.05 - sin 0 ]

Or, v = 10 + 0.132 [ 0 - 0 ]

∴  v = 10 volts

Again

Power = v × i

i.e p = 10 × ( 5 cos 60πt )

or, p = 50 cos 0.3π

Or, p = 50 × 0.58

∴  Power = 29. 7 watt

Hence, The power is 29.7 watt  Answer