Cut-in voltage or knee voltage or threshold voltage is the minimum voltage( in forward bias condition)after which the diode current rises rapidly and diode is said to be conducting
And here we are given that the diode forward biased resistance is 10 ohm and the external resistance is 20 ohm
current = "\\frac{V-V_{cut\\ in}}{R_{total}}=\\frac{V-0.5}{10+20}=\\frac{V-0.5}{30}"
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