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Answer:
The resistors will be in parallel to produce a net resistance of 4ohm and current in 20 ohm resistor will be 0.5A and 5ohm resistor will be 2A.
Explanation:
We are given 10 voltage power source and we have two Resistors with resistance of 20 ohm and 5ohm.
We need to find the orientation in which these two resistors would be arranged so that the circuit could get a current of 2.5Ampere.
Using ohm's law we have
V = I*R
V= voltage
I= current
R= resistance
10 = 2.5*R
R = 10/2.5 = 4ohm
that means we need a total of 4ohm resistance from these two resistors.
since the net Resistance(4ohm) is lower than the smallest resistance(5ohm) available that means the orientation of the resistors will be in parallel.
[tex]\frac{1}{R} = \frac{1}{R1} +\frac{1}{R2}\\ = \frac{1}{20} +\frac{1}{5}\\ \\ = \frac{1+4}{20} =\frac{1}{4}[/tex]
R(net) =4ohm
Now the orientation of the resistors are in parallel so the current will be divided.
we know that the current will divide in opposite manner the arm which provides more resistance less current will flow from there and vice versa.
We know that the voltage in parallel remains same
In 20 ohm resistance
again using ohms law
V = i1*R1
10 = i1*20
i1 = 0.5A
in 5ohm resistor
V=i2*R2
10 = I2*5
i2 =2A
and i1+i2 = 0.5+2= 2.5A which means our calculation is correct.
Therefore the resistors will be in parallel to produce a net resistance of 4ohm and current in 20 ohm resistor will be 0.5A and 5ohm resistor will be 2A.
Both the resistors will be arranged in parallel and currents in 20 ohm and 5 ohm will be 0.5A and 2A respectively
Ohm's Law and resistors arranged in parallel or series:
- Ohm's Law → V = iR
Here, V = Voltage
i = current
R = Resistance
- If two resistors R₁ and R₂ are arranged in series,
Resultant resistance will be represented by,
R = R₁ + R₂
- If these resistors are attached in parallel,
[tex]\frac{1}{R} =\frac{1}{R_1} +\frac{1}{R_2}[/tex]
[tex]\frac{1}{R}=\frac{R_1+R_2}{R_1R_2}[/tex]
[tex]R=\frac{R_1R_2}{R_1+R_2}[/tex]
Given in the question,
- Voltage of power supply 'V' = 10V
- [tex]R_1=20[/tex] ohm and [tex]R_2=5[/tex] ohm
Resultant resistance when arranged in series,
[tex]R=20+5=25[/tex] ohm
By using Ohm's Law,
V = ir
10 = 25i
i = 0.4 A
But the current is 2.5A therefore, resistors will not be arranged in series.
If the resistors are arranged in parallel,
[tex]R=\frac{(20)(5)}{20+5}=4[/tex] ohm
By using Ohm's Law,
V = ir
10 = 4i
i = 2.5 A
Therefore, resistors will be joined in parallel.
Since, "voltage in each resistor arranged in parallel is same"
V = i₁R₁
10 = i₁.(20)
i₁ = 0.5A
For second resistor,
V = i₂R₂
10 = i₂(5)
i₂ = 2A
Therefore, both the resistors will be arranged in parallel and currents in 20 ohm and 5 ohm will be 0.5A and 2A respectively.
Learn more about the Ohm's law here,
https://brainly.com/question/12600154?referrer=searchResults
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