Electric current through a conductor varies with time as It - 50 sin100- t- Here I is in ampere and and t in seconds- Total charge that passes any point from t - 0 to t - 1-200s is

Given, #10; #10; I=50sin( 100π t #10;) #10; #10; dQ=Idt=50sin( 100π #10;t )dt #10; #10; #10;Q=∫_0^1/20050sin( 100π t )dt=. 50× # ...

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Standard XII

Mathematics

Basic Inverse Trigonometric Functions

Electric curr...

Question

Electric current through a conductor varies with time as I(t) = 50 $s i n (100 π t)$ .
Here I is in ampere and and t in seconds. Total charge that passes any point from t = 0 to t = $\frac{1}{200} s$ is

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Solution

Given,

$I = 50 sin (100 π t)$

$d Q = I d t = 50 sin (100 π t) d t$

$Q = \int_{0}^{\frac{1}{200}} 50 sin (100 π t) d t = {50 \times 100 π cos (100 π t) |}_{0}^{\frac{1}{200}}$

$Q = 50 \times 100 π = 5000 π C$

Hence, total charge is $5000 π C$

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Electric current through a conductor varies with time as I(t) = 50 sin(100πt). Here I is in ampere and and t in seconds. Total charge that passes any point from t = 0 to t = 1200s is

Given, I=50sin(100πt) dQ=Idt=50sin(100πt)dt Q=∫1200050sin(100πt)dt=50×100πcos(100πt)|12000 Q=50×100π=5000πC Hence, total charge is 5000πC

Electric current through a conductor varies with time as I(t) = 50 $s i n (100 π t)$ .
Here I is in ampere and and t in seconds. Total charge that passes any point from t = 0 to t = $\frac{1}{200} s$ is

Given,

$I = 50 sin (100 π t)$

$d Q = I d t = 50 sin (100 π t) d t$

$Q = \int_{0}^{\frac{1}{200}} 50 sin (100 π t) d t = {50 \times 100 π cos (100 π t) |}_{0}^{\frac{1}{200}}$

$Q = 50 \times 100 π = 5000 π C$

Hence, total charge is $5000 π C$