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Tom [10]
4 years ago
14

An electric current in a conductor varies with time according to the expression i(t) = 110 sin (120πt), where i is in amperes an

d t is in seconds. what is the total charge passing a given point in the conductor from t = 0 to t = 1/180 s?
Physics
2 answers:
Dafna1 [17]4 years ago
6 0

As we know that current is defined as rate of flow of charge

i = \frac{dq}{dt}

so by rearranging the equation we can say

q = \int i dt

here we know that

i(t) = 110 sin(120\pi t)

here we will substitute it in the above equation

q = \int 110 sin(120\pi t) dt

q = 110 [- \frac{cos(120\pi t)}{120\pi}]

now here limits of time is from t = 0 to t = 1/180s

so here it will be given as

q = \frac{110}{120\pi}( -cos0 + cos(\frac{2\pi}{3}))

q = 0.44 C

so total charge flow will be 0.44 C

ANEK [815]4 years ago
6 0

Answer:

The total charge passing a given point in the conductor is 0.438 C.

Explanation:

Given that,

The expression of current is

i(t)=110\sin(120\pi t)

\dfrac{dq(t)}{t}=110\sin(120\pi t)

dq(t)=110\sin(120\pi t)dt....(I)

We need to calculate the total charge

On integrating both side of equation (I)

\int_{0}^{q}dq(t)=\int_{0}^{\dfrac{1}{180}}110\sin(120\pi t)dt

q=110(\dfrac{-\cos(120\pi t)}{120\pi})_{0}^{\dfrac{1}{180}}

q=-\dfrac{110}{120\pi}(cos(120\pi(\dfrac{1}{180}))-\cos120\pi(0))

q=-0.2918(-\dfrac{1}{2}-1)

q=0.438\ C

Hence,  The total charge passing a given point in the conductor is 0.438 C.

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