Answer:
a) 201
b) 0
Explanation:
note:
solution is attached in word form due to error in mathematical equation. furthermore i also attach Screenshot of solution in word due to different version of MS Office please find the attachment
For the time interval from 0 to 2, sine wave reaches to zero for 201 times. Hence the current equals to zero for 201 times.
No charge transported through the light in the first second.
Given that, the current flowing through the bulb is [tex]I(t)=114 sin (100\pi t) \;\rm A[/tex].
The general equation of the current is,
[tex]I(t) =Asin(2\pi ft)[/tex]
So the frequency can be calculated as,
[tex]2\times \pi\times f\times t = 100\times \pi[/tex]
[tex]f =50 \;\rm Hz[/tex]
Hence the frequency of the sine wave is 50 Hz.
For the time interval from 0 to 2, the number of zero for the sine wave is,
[tex]No.\;of\; zero = (2\times50\times2 )+1[/tex]
[tex]No.\;of\;zero=201[/tex]
So, For the time interval from 0 to 2, sine wave reaches to zero for 201 times. Hence the current equals to zero for 201 times.
The charge can be calculated by the formula given below.
[tex]Q(t) = \int\limits^{t_1}_{t_2} {I(t)} \ dt[/tex]
[tex]Q(t)=\int\limits^1_0 {114sin(100\pi t)} \ dt[/tex]
[tex]Q(t) = \dfrac {-114cos(100\pi t)}{100\pi}[/tex]
[tex]Q(t) = \dfrac {-114cos(100\pi \times 1)}{100\pi}-\dfrac {-114cos(100\pi \times0)}{100\pi}[/tex]
[tex]Q(t)=0[/tex]
Hence, no charge transported through the light in the first second.
For more details, follow the link given below.
https://brainly.com/question/1345174.
