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### JEE Main 2021 (Online) 27th August Evening Shift

Numerical
An ac circuit has an inductor and a resistor resistance R in series, such that XL = 3R. Now, a capacitor is added in series such that XC = 2R. The ratio of new power factor with the old power factor of the circuit is $$\sqrt 5 :x$$. The value of x is ___________.

## Explanation $$\cos \phi = {R \over {\sqrt {{R^2} + 3{R^2}} }}$$

$$= {1 \over {\sqrt {10} }}$$

$$\cos \phi ' = {R \over {\sqrt {{R^2} + {R^2}} }}$$

$$= {1 \over {\sqrt 2 }}$$

$${{\cos \phi '} \over {\cos \phi }} = {{\sqrt {10} } \over {\sqrt 2 }} = {{\sqrt 5 } \over 1}$$

$$\therefore$$ x = 1
2

### JEE Main 2021 (Online) 27th August Morning Shift

Numerical
The alternating current is given by $$i = \left\{ {\sqrt {42} \sin \left( {{{2\pi } \over T}t} \right) + 10} \right\}A$$

The r.m.s. value of of this current is ................. A.

## Explanation

$$f_{rms}^2 = f_{1\,rms}^2 + f_{2\,rms}^2$$

$$= {\left( {{{\sqrt {42} } \over {\sqrt 2 }}} \right)^2} + {10^2}$$

$$= 121 \Rightarrow {f_{rms}}$$ = 11 A
3

### JEE Main 2021 (Online) 27th July Evening Shift

Numerical
In the given figure the magnetic flux through the loop increases according to the relation $$\phi$$B(t) = 10t2 + 20t, where $$\phi$$B is in milliwebers and t is in seconds.

The magnitude of current through R = 2$$\Omega$$ resistor at t = 5 s is ___________ mA. ## Explanation

$$\left| \in \right| = {{d\phi } \over {dt}}$$ = 20t + 20 mV

$$\left| i \right| = {{\left| \in \right|} \over R}$$ = 10t + 10 mA

at t = 5

$$\left| i \right|$$ = 60 mA
4

### JEE Main 2021 (Online) 27th July Morning Shift

Numerical
Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then T1 is connected to T2. As the current in R = 6$$\Omega$$ attains a maximum value of steady state level, T1 is disconnected from T2 and immediately connected to T3. Potential drop across r = 3$$\Omega$$ resistor immediately after T1 is connected to T3 is __________ V. (Round off to the Nearest Integer) ## Explanation

What T1 and T2 are connected, then the steady state current in the inductor $$I = {6 \over 6} = 1A$$

When T1 and T3 are connected then current through inductor remains same. So potential difference across 3$$\Omega$$

V = Ir = 1 $$\times$$ 3 = 3 Volt

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