Consider the circuit in Figure 2.4. The input voltage is
a.
The minimum value of the resistance of a battery charger circuit for a given peak battery charging current.
Answer to Problem 2.1TYU
Minimum resistance is
Explanation of Solution
Given Information:
The given values are:
Range of voltage
Calculation:
The battery charger circuit contains a half-wave rectifier as shown below.
Using the Kirchhoff’s Voltage Law, voltage across the resistor is given by,
The current through the resistor,
The peak current through the resistor (or the diode),
The diode current will be maximum when the input voltage is maximum at
From equation (1)
Then, equation (2) can be written as,
Then the minimum value of the resistor,
Substituting the values,
Conclusion:
The minimum resistance value is
b.
The range in peak current and the range in a fraction of cycle diode conducts.
Answer to Problem 2.1TYU
The range in peak current is,
The range in duty cycle is
Explanation of Solution
Given Information:
Calculation:
Here the battery charger circuit contains a halfwave rectifier and the circuit can be drawn as below. The range for the battery voltage is
Using the Kirchhoff’s Voltage Law,
It is known that,
The voltage through the resistor,
Then equation (1) can be written as,
The range for the peak current through the diode,
When the diode is forward biased and at the time diode start conducting, let’s say
Substitute the values
By symmetry, the point where
Then fraction of the time diode is conducting can be calculated as,
Hence,
Conclusion:
The range in peak current is,
The range in the duty cycle is
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