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A 9 V stabilised voltage supply is required to run a car stereo system from its 12 V battery. Zener diode with V_Z = 9 V and P_max = 0.27 W is used as the voltage regulator in the circuit shown below. If the load resistance is $450 Ω,$ then find the value of series resistor:

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$100 Ω$

$90 Ω$

$60 Ω$

$150 Ω$

answer is A.

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Detailed Solution

Zener current,

$I_{Z} = \frac{P_{max}}{V_{max}} = \frac{0.27}{9} = 0.03 A$

Current through $R_{L} = \frac{9}{450} = 0.02 A$

Current drawn from the battery,

$I = I_{L} + I_{Z} = 0.02 + 0.03 = 0.05 A$

$∴$ Series resistor,

$R_{S} = \frac{(V)_{R_{S}}}{I} = \frac{3}{0.05} = 60 Ω$

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