A dc battery with an internal resistance of 1 is to be charged from a constant de source of 220 V. The battery is to be charged from its internal emf of 90 V to 122 V. The charging current to be remained constant at 10 A. The range of the duty cycle is.
(a) 0.454 to 0.60
(b) 0.415 to 0.54
(c) 0.392 to 0.02
(d) 0.421 to 0.68
Answers
Answer:
a) Duty cycle is 0.454 to 0.60
Step-by-step explanation:
According to the information provided in the question it is given as
A dc battery with an internal resistance of 1 is to be charged from a constant d c source of 220 V. The battery is to be charged from its internal emf of 90 V to 122 V. The charging current to be remained constant at 10 A.
We need to find the range of the duty cycle is
Let us assume
E=8 V,
Internal resistance= R 1=0.5Ω
V=120 V,
Resistance R 2=15.5Ω
Now putting the formula of effective voltage we get
Effective voltage V′=V−E=112 V
Also
I=R 1 + R 2 V′=7 A
And the voltage across R 1 is
R 1=IR 1=3.5 V
By putting the values in formula terminal voltage
Terminal voltage
=8+3.5= 11.5 V
Because of the internal resistance of 1 is to be charged so the range of the duty cycle is 0.454 to 0.60
Note: A series resistor in the charging circuit limits the current drawn From the external source. in its absence, the current will be dangerously High.
Given,
The internal resistance of DC battery = 1
Power of source = 220v
internal emf = 90 V to 122 V
Changing current to remain constant at = 10A
To find,
Range of the duty cycle
Solution,
Assuming E = 8V
Internal resistance = 0.5Ω
V = 120V
Resistance = 15.5Ω
Effective voltage = V−E=112 V
Also
I=R 1 + R 2 V′=7 A
And the voltage across R 1 is
R 1=IR 1=3.5 V
By putting the values in formula terminal voltage
Terminal voltage = 8 + 3.5 = 11.5 V
So, as the internal resistance is 1, the range of the duty cycle will be 0.454 to 0.60
Thus, the range of the duty cycle will be 0.454 to 0.60