Respuesta :
Answer: The correct answer is Option D.
Explanation:
To calculate the value of resistor used in parallel circuit, we need to follow some steps:
- Step 1: Calculation of Voltage from series circuit.
For the calculation of voltage, we will use thew equation given by Ohm's Law, which is:
[tex]V=IR[/tex] ....(1)
where,
V = voltage = ?V
I = Current flowing = 1.6 A
R = Resistance = (5 + 5) = 10 ohm (In Series, resistance gets added up)
Putting values in above equation, we get:
[tex]V=1.6\times 10=16V[/tex]
- Step 2: Finding the total resistance from parallel circuit
As, the voltage passing through the resistors remains the same. Hence, the above voltage can be used:
I = 2A
V = 16V
Putting values in equation 1, we get:
[tex]16=2\times R_{parallel}\\\\R_{parallel}=8\Omega[/tex]
- Step 3: Finding the value of each resistor.
We are given 3 identical resistors that are connected in parallel. In parallel, the total resistance is calculated by using the formula:
[tex]\frac{1}{R_{parallel}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\\\\R_1=R_2=R_3=R\\\\\frac{1}{R_{parallel}}=\frac{1+1+1}{R}=\frac{3}{R}[/tex]
Putting values in above equation, we get:
[tex]\frac{1}{8}=\frac{3}{R}\\\\R=24\Omega[/tex]
Hence, the correct answer is Option D.
The overall resistance is the ratio of overall voltage and the overall current flowing in the circuit by the Ohm's law.
The value of a resistor used in the parallel circuit is 24 ohms.
What is the Ohm's law?
Ohm's law states that for a flowing current the potential difference of the circuit is directly proportional to the current flowing in it. Thus,
[tex]V\propto I[/tex]
Here, [tex]V[/tex] is the potential difference and [tex]I[/tex] is the current.
It can be written as,
[tex]V+IR[/tex]
Here, [tex]R[/tex] is the resistance of the circuit.
Given information-
The power source provides a current of 1.6 A.
The resistance of power source is 5 ohms.
The overall current in the circuit is 2.0 A.
As 2 resistors of 5 ohms connected in series. The overall resistance of is sum of all the series connected of resistors. Thus the overall resistance is,
[tex]R=5+5\\R=10 \rm ohms[/tex]
Put the values in the above formula to find the voltage as,
[tex]V=1.6\times10\\V=16\rm Volts[/tex]
Thus the voltage of the power source is 16 volts.
Now three identical resistors connected In the parallel circuit. The overall resistance of the parallel connection is calculated by,
[tex]\dfrac{1}{R_{}ovrall}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}\\[/tex]
As all the resistance has same value thus,
[tex]\dfrac{1}{R_{}ovrall}=\dfrac{3}{R}[/tex]
As the overall resistance is the ratio of overall voltage and the overall current flowing in the circuit by the Ohm's law. Thus,
[tex]\dfrac{I{overall}}{V_{}ovrall}=\dfrac{3}{R}\\\dfrac{2}{16}=\dfrac{3}{R}\\R=24\rm ohms[/tex]
Hence, the value of a resistor used in the parallel circuit is 24 ohms.
Learn more about the Ohm's law here;
https://brainly.com/question/25822112
