JEE MAIN - Physics (2019 - 8th April Evening Slot - No. 5)
A circuit connected to an ac source of emf
e = e0sin(100t) with t in seconds, gives a phase
difference of $$\pi $$/4 between the emf e and
current i. Which of the following circuits will
exhibit this ?
RC circuit with R = 1 k$$\Omega $$ and C = 1μF
RL circuit with R = 1k$$\Omega $$ and L = 1mH
RC circuit with R = 1k$$\Omega $$ and C = 10 μF
RL circuit with R = 1 k$$\Omega $$ and L = 10 mH
Explanation
Given phase difference = $${\pi \over 4}$$ and $$\omega $$ = 100 rad/s
$$ \Rightarrow $$ Reactance (X) = Resistance (R) Now by checking option.
Option (A)
R = 1000 $$\Omega $$ and Xc = $${1 \over {{{10}^{ - 6}} \times 100}} = {10^4}\Omega $$
Option (B)
R = 103 $$\Omega $$ and XL = $${10^{ - 3}} \times 100 = 10^{-1} \Omega $$
Option (C)
R = 103 $$\Omega $$ and Xc = $${1 \over {{10 \times {10}^{ - 6}} \times 100}} = {10^3}\Omega $$
Option (D)
R = 103 $$\Omega $$ and XL = $$10 \times {10^{ - 3}} \times 100 = 1\Omega $$
$$ \Rightarrow $$ Reactance (X) = Resistance (R) Now by checking option.
Option (A)
R = 1000 $$\Omega $$ and Xc = $${1 \over {{{10}^{ - 6}} \times 100}} = {10^4}\Omega $$
Option (B)
R = 103 $$\Omega $$ and XL = $${10^{ - 3}} \times 100 = 10^{-1} \Omega $$
Option (C)
R = 103 $$\Omega $$ and Xc = $${1 \over {{10 \times {10}^{ - 6}} \times 100}} = {10^3}\Omega $$
Option (D)
R = 103 $$\Omega $$ and XL = $$10 \times {10^{ - 3}} \times 100 = 1\Omega $$
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