GATE EC 2016 Set 1 — Question 43
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Analog Circuits → Circuit Fundamentals & Theorems → HW, FW & Bridge Rectifiers
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Question
An AC voltage source volts is applied to the following network. Assume that , and , and that the diode is ideal.
RMS current (in mA) through the diode is ________
Correct answer
0.9 to 1.1
Solution
The given circuit consists of an AC source and an ideal diode in series with a resistive network. The diode conducts only during the positive half-cycle of the input voltage.Step 1: Determine the peak current ()
The peak voltage of the source is V. Let be the equivalent resistance of the network as seen from node 'a' to ground. The peak current through the diode is given by:Step 2: Calculate the RMS current ()
For a half-wave rectified sinusoidal current, the RMS value is half of the peak value:Step 3: Find the equivalent resistance ()
By analyzing the resistor network using series-parallel reduction and symmetry (nodes and are at the same potential, as are nodes and ), the equivalent resistance is calculated to be .Step 4: Final CalculationThe value of is mA, which falls within the specified range of to .
The peak voltage of the source is V. Let be the equivalent resistance of the network as seen from node 'a' to ground. The peak current through the diode is given by:Step 2: Calculate the RMS current ()
For a half-wave rectified sinusoidal current, the RMS value is half of the peak value:Step 3: Find the equivalent resistance ()
By analyzing the resistor network using series-parallel reduction and symmetry (nodes and are at the same potential, as are nodes and ), the equivalent resistance is calculated to be .Step 4: Final CalculationThe value of is mA, which falls within the specified range of to .
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