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1

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

Numerical
A zener diode of power rating 2W is to be used as a voltage regulator. If the zener diode has a breakdown of 10 V and it has to regulate voltage fluctuated between 6 V and 14 V, the value of Rs for safe operation should be ___________ $$\Omega$$. ## Explanation

When unregulated voltage is 14 V voltage across zener diode must be 10 V. So potential difference across resistor $$\Delta$$VRs = 4V

and Pzener = 2W

VI = 2

I = $${2 \over {10}}$$ = 0.2 A

$$\Delta$$VRs = I Rs

4 $$\times$$ 0.2 Rs $$\Rightarrow$$ Rs = $${40 \over {2}}$$ = 20$$\Omega$$
2

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

Numerical
A circuit is arranged as shown in figure. The output voltage V0 is equal to ................... V. ## Explanation

As diodes D1 and D2 are in forward bias, so they acted as negligible resistances

$$\Rightarrow$$ Input voltage become zero $$\Rightarrow$$ Input current is zero

$$\Rightarrow$$ Output current is zero

$$\Rightarrow$$ V0 = 5 volt
3

### JEE Main 2021 (Online) 26th August Evening Shift

Numerical
For the given circuit, the power across Zener diode is .............. mW. ## Explanation $$i = {{10V} \over {5k\Omega }}$$ = 2mA

$$I = {{14V} \over {1k\Omega }}$$ = 14 mA

$$\therefore$$ Iz = 12 mA

$$\therefore$$ P = IzVz = 120 mW
4

### JEE Main 2021 (Online) 26th August Evening Shift

Numerical
If the maximum value of accelerating potential provided by a ratio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ...............

[mp = 1.67 $$\times$$ 10$$-$$27 kg, e = 1.6 $$\times$$ 10$$-$$19C, Speed of light = 3 $$\times$$ 108 m/s]

## Explanation

V = 12 kV

Number of revolution = n

$$n[2 \times {q_P} \times V] = {1 \over 2}{m_P} \times v_P^2$$

$$n[2 \times 1.6 \times {10^{ - 19}} \times 12 \times {10^3}]$$

$$= {1 \over 2} \times 1.67 \times {10^{ - 27}} \times {\left[ {{{3 \times {{10}^8}} \over 6}} \right]^2}$$

n(38.4 $$\times$$ 10$$-$$16) = 0.2087 $$\times$$ 10$$-$$11

n = 543.4

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