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Harman [31]
3 years ago
5

The half-wave rectifier circuit of vs(t) = 170 sin(377t) V and a load resistance R = 15Ω. Determine: a. The average load current

. b. The rms load current. c. The power absorbed by the load. d. The apparent power supplied by the source. e. The power factor of the circuit.
Physics
2 answers:
irina1246 [14]3 years ago
6 0

Answer:

a  average load current = 11.33 A

b rms load current = 8.02A

c true power =962.64 W

d apparent power =962.64 W

e. power factor cosθ =1

Explanation:

Vs (t) = 170 sin(377t) v

Vm =170v

Vrms = 170/√2 =120.23 v

Im = Vm/R = 170/15 = 11.33 A

Irms = Im/ √2 = 11.33/√2 =8.02A

Resistors are electronic components that consume energy

the power in a resistor is given by  P =IVcosθ ; in a resistor cosθ =1

P =IV

The electrical power consumed by a resistance, (R) is called the true or real power

and is obtained by multiplying the rms voltage with the rms current.

P= Vrms × Irms

120.03×8.02

P= 962.64 W ; true power

apparent power = Vrms × Irms

=120.03×8.02

= 962.64W ; apparent power

power factor cosθ = true power/ apparent power

cosθ = 962.64/962.64

cosθ = 1

For the purely resistive circuit, the power factor is 1 , because the reactive power is equal to zero (0).

Natasha_Volkova [10]3 years ago
4 0

Answer:

The instantaneous voltage (V_{s}) across the half-wave rectifier is given by

V_{s}(t) = V_{m}cos(wt + θ) V    ------------ (i)

Where V_{m} is the peak voltage and Θ is the phase angle.

Given:

V_{s}(t) = 170sin(377t) V    -------------------------(ii)

Load Resistance R = 15Ω

Comparing equations (i) and (ii)

V_{m} = 170V

(a) Average load current I_{0} = \frac{V_{0}}{R} = \frac{V_{m} }{\pi R}

Taking pi as 22/7 and substituting the values of R and V_{m} into the above equation, we have;

I_{0} = \frac{170}{\pi * 15} = 3.6A

(b) The rms load current I_{rms} = \frac{V_{m}}{2R}

Substituting the values of R and V_{m} into the equation above gives;

I_{rms} = \frac{170}{2 * 15} = 5.67A

(c). Power absorbed by the load is given by the ac and the dc.

Dc Power absorbed = \frac{V_{m} ^{2} }{\pi^{2} * R } = \frac{170^{2} }{\pi ^{2} * 15} = 195W

Ac Power absorbed = \frac{V_{rms} ^{2} }{R}

where V_{rms} = \frac{V_{m} }{2} = \frac{170}{2} = 85V

Therefore, Ac Power absorbed = \frac{85^{2} }{15} = 481.67W

(d) Apparent Power is the product of the rms values of the current and the voltage.

Apparent Power = I_{rms} * V_{rms}

Apparent Power = 5.67 * 85 = 481.95W

(e) Power factor is the ratio of the Power absorbed by load to the Apparent Power

Therefore Power factor = \frac{Power  absorbed}{Apparent Power}

Power factor = \frac{481.67}{481.95} = 0.999

PS: Power absorbed could also be called the real power

<em>Hope this helps</em>

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