Question

The electron beam in a TV picture tube carries 1015 electrons per second. As a design engineer, determine the voltage needed to accelerate the electron beam to achieve 4 W.

Answer 1

Answer:

The voltage needed to accelerate the electron beam is 2.46 x 10^16 Volts

Explanation:

The rate of electron flow is given as:

q = 1015 electrons per second

The total current is given by:

Total Current = (Rate of electron flow)(Charge on one electron)

Total Current = I = (1015 electrons/s)(1.6 x 10^-19 C/electron)

I = 1.624 x 10^-16 A

Now, we know that electric power is given as:

Electric Power = Current x Voltage

P = IV

V = P/I

V = 4 W/1.624 X 10^-16 A

V = 2.46 x 10^16 Volts

Answer 2

The voltage needed to accelerate the electron beam to achieve 4 W is; V = 25 kV

We are given;

Rate of flow of electrons; dn/dt = 10^(15) electrons/s

We know that amount of electron flow is given by; q = ne

Where;

n is number of elecrons

e is electron charge = 1.6 × 10^(-19) C

Now, we know that formula for current here is;

I = e(dn/dt)

Thus,

I = 1.6 × 10^(-19) × 10^(15)

I = 1.6 × 10^(-4) A

Now, we are given power = 4 W

Formula for voltage is;

V = P/I

Thus;

V = 4/(1.6 × 10^(-4))

V = 25000 V

V = 25 kV

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