In a certain circuit, current changes with time according to i=2 √t. R.m.s. value of current between t=2 s to t=4 s will be

Question

In a certain circuit, current changes with time according to i=2 √t. R.m.s. value of current between t=2 s to t=4 s will be (A) 3 A (B) 3 √3 A (C) 2 √3 A (D) (2-√2) A

Tardigrade Admin · Accepted Answer

overlinei2=(∫ i2 d t/∫ d t)=(∫ limits24(4 t) d t/∫ limits24 d t)=(4 ∫ limits24 t d t/2) =2[(t2/2)]24=[t2]24=12 ⇒ i rms =√i2=√12=2 √3 A

Q. In a certain circuit, current changes with time according to $i = 2 t$ . R.m.s. value of current between $t = 2 s$ to $t = 4$ s will be

3 A

$33 A$

$23 A$

$(2 - 2) A$

$\overline{i^{2}} = \frac{\int i ^{2} d t}{\int d t} = \frac{2 \int 4 ( 4 t ) d t}{2 \int 4 d t} = \frac{4 2 \int 4 t d t}{2}$
$= 2 [\frac{t ^{2}}{2}]_{2}^{4} = [t^{2}]_{2}^{4} = 12$
$\Rightarrow i_{r m s} = i^{2} = 12 = 23 A$

Q. In a certain circuit, current changes with time according to i=2t​. R.m.s. value of current between t=2s to t=4 s will be

3 A

33​A

23​A

(2−2​)A

i2=∫dt∫i2dt​=2∫4​dt2∫4​(4t)dt​=242∫4​tdt​ =2[2t2​]24​=[t2]24​=12 ⇒irms​=i2​=12​=23​A

Q. In a certain circuit, current changes with time according to $i = 2 t$ . R.m.s. value of current between $t = 2 s$ to $t = 4$ s will be

$33 A$

$23 A$

$(2 - 2) A$

$\overline{i^{2}} = \frac{\int i ^{2} d t}{\int d t} = \frac{2 \int 4 ( 4 t ) d t}{2 \int 4 d t} = \frac{4 2 \int 4 t d t}{2}$
$= 2 [\frac{t ^{2}}{2}]_{2}^{4} = [t^{2}]_{2}^{4} = 12$
$\Rightarrow i_{r m s} = i^{2} = 12 = 23 A$