Answer:
Option D.
Resistance (R) decreases
Voltage (V) is constant
Current (I) increases
Explanation:
We'll begin by writing an equation relating resistance and diameter of a wire. This is given below:
R = ρL/A ......... (1)
A = πr² (since the wire is circular in shape)
r = d/2
A = πr² = π(d/2)²
A = πd²/4
Substitute the value of A into equation 1
R = ρL/A
R = ρL ÷ A
R = ρL ÷ πd²/4
R = ρL × 4/πd²
R = 4ρL /πd²
Where:
R is the resistance of the wire.
ρ is the resistivity of the wire.
L is the length of the wire.
A is the cross sectional area of the wire.
r is the radius.
d is the diameter of the wire
From equation (1) above, we can say that the resistance (R) is inversely proportional to the square of the diameter of the wire. This implies that an increase in the diameter of the wire will result in a decrease of the resistance. Also, a decrease in the diameter of the wire will result in an increase in the resistance of the wire.
1. Since the diameter of the wire is increase, therefore, the resistance of the wire will decrease.
2. From ohm's law,
V = IR
Divide both side by I
R = V/I
Where:
R is the resistance
V is the voltage
I is the current
From the above equation, the resistance (R) is directly proportional to the voltage (V) and inversely proportional to the current (I).
If we keep the voltage constant, this means that an increase in the resistance will lead to a decrease in the current. Also, a decrease in the resistance will lead to an increase in the current.
Since the resistance of the wire decrease, the current will increase.
From the illustrations made above, an increase in the diameter of the wire will lead to:
1. Decrease in resistance.
2. Voltage is constant.
3. Increase in current.
