For a type A chopper- source voltage Vs-220 V- chopping frequency f-500 Hz- Ton-800 - s- R -1- -L-1 mH and E-72 V- The duty cycle - at the limit of continuous conduction is

The duty cycle α at the limit of continuous conduction is α '=T_aTln [ 1+m ( e^T/T_a 1 ) ] T_a=LR=1× 10^ 31=1× 10^ 3 s m=EV_s=72220=0.3272 T=1f=1500=2× 10^ 3s ...

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Standard XI

Physics

Capacitive Reactance

For a type A ...

Question

For a type A chopper, source voltage $V_{s} = 220 V,$ chopping frequency $f = 500 H z, T_{o n} = 800 μ s, R = 1 Ω, L = 1 m H$ and $E = 72 V$ . The duty cycle $α$ at the limit of continuous conduction is
0.56

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Solution

The correct option is A 0.56
The duty cycle $α$ at the limit of continuous conduction is
$α^{'} = \frac{T_{a}}{T} l n [1 + m (e^{T / T_{a}} - 1)]$
$T_{a} = \frac{L}{R} = \frac{1 \times 10^{- 3}}{1} = 1 \times 10^{- 3} s$
$m = \frac{E}{V_{s}} = \frac{72}{220} = 0.3272$
$T = \frac{1}{f} = \frac{1}{500} = 2 \times 10^{- 3} s$
Duty cycle, $α^{'} = (\frac{1 \times 10^{- 3}}{2 \times 10^{- 3}}) l n ⎡ ⎢ ⎢ ⎢ ⎣ 1 + 0.3272 ⎛ ⎜ ⎜ ⎜ ⎝ e^{(\frac{2 \times 10^{- 3}}{1 \times 10^{- 3}})} - 1 ⎞ ⎟ ⎟ ⎟ ⎠ ⎤ ⎥ ⎥ ⎥ ⎦$
$α^{'} = 0.564$

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For a type A chopper, source voltage Vs=220V, chopping frequency f=500Hz, Ton=800μs, R=1Ω,L=1mH and E=72V. The duty cycle α at the limit of continuous conduction is0.56

For a type A chopper, source voltage $V_{s} = 220 V,$ chopping frequency $f = 500 H z, T_{o n} = 800 μ s, R = 1 Ω, L = 1 m H$ and $E = 72 V$ . The duty cycle $α$ at the limit of continuous conduction is
0.56