Answer:
The new current will be 18 ampere
Explanation:
1- getting the initial resistance of the wire:
Based on Ohm's law:
[tex]Voltage = Current * Resistance[/tex]
We are given that:
At V=10 volts, the current is 2A
This means that:
10 = 2*R
R₁ = 5 ohm
2- getting the final resistance of the wire:
Resistance, resistivity and area of a wire are connected by the following rule:
[tex]Resistance = \frac{resistivity * length}{Area}[/tex]
We also know that the area of the cylinder is πr²
Therefore:
[tex]Resistance = \frac{resistivity * length}{\pi r^2 }[/tex]
This means that at constant resistivity and length, the resistance of the material is inversely proportional to the square of its radius
In other words:
At constant resistivity and length: [tex]\frac{R_{1} }{R_{2}} = \frac{(r_{1})^2 }{(r_{2})^2 }[/tex]
where R stands for resistance and r stands for radius
Now, we are given that the diameter is tripled, this means that the radius id tripled as well.
Substituting in the above equation :
[tex]\frac{R_{1}}{R_{2}} = \frac{(r_{1})^2 }{(3r_{1})^2 }[/tex] [tex]=\frac{1}{9}[/tex]
This means that:
New resistance = old resistance / 9
New resistance = 5/9 ohm
3- getting the final current:
Again, using ohm's law, we have:
Voltage is unchanged = 10 volts
Resistance = 5/9 ohm
Therefore:
[tex]V=I*R\\\\10 = \frac{5}{9} * I\\ \\I = 18 ampere[/tex]
Hope this helps :)
If the diameter of this resistor is now tripled, the current will be 18 A
Electrical circuits can generally be divided into two types , i.e :
In series circuit, the electric current flowing on each resistor is always the same as the total current.
To find the total resistances you can use the following formula:
[tex]\large {\boxed {R_s = R_1 + R_2 + R_3 + ...} }[/tex]
In parallel circuits, the electrical voltage at each resistor is always the same as the source voltage.
To find the total resistances you can use the following formula:
[tex]\large {\boxed {\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...} }[/tex]
Let's tackle the problem now !
Given:
Potential Difference = V = 10 V
Current = I = 2 A
Diameter = d' = 3d
Unknown:
I' = ?
Solution:
This problem is about Resistivity.
[tex]I : I' = \frac{V}{R} : \frac{V}{R'}[/tex]
[tex]I : I' = \frac{1}{R} : \frac{1}{R'}[/tex]
[tex]I : I' = R' : R[/tex]
[tex]I : I' = \rho \frac{L}{A'} : \rho \frac{L}{A}[/tex]
[tex]I : I' = \frac{1}{A'} : \frac{1}{A}[/tex]
[tex]I : I' = A : A'[/tex]
[tex]I : I' = \frac{1}{4} \pi d^2 : \frac{1}{4} \pi (d')^2[/tex]
[tex]I : I' = d^2 : (d')^2[/tex]
[tex]I : I' = d^2 : (3d)^2[/tex]
[tex]I : I' = d^2 : 9d^2[/tex]
[tex]I : I' = 1 : 9[/tex]
[tex]I' = 9I[/tex]
[tex]I' = 9(2)[/tex]
[tex]I' = 18 ~ A[/tex]
Grade: High School
Subject: Physics
Chapter: Current of Electricity
Keywords: Series , Parallel , Measurement , Absolute , Error , Combination , Resistor , Resistance , Ohm
