Question:

A wire with a length of 2 meters and a resistance of 10 ohms is connected to a battery with a voltage of 20 volts. Calculate the current flowing through the wire.

Answer:

The current flowing through a wire can be calculated using Ohm's Law, which states that the current (I) is equal to the voltage (V) divided by the resistance (R).

Ohm's Law equation: I = V / R

Given:

• Length of wire (L) = 2 meters
• Resistance of wire (R) = 10 ohms
• Voltage of battery (V) = 20 volts

We can use the formula R = ρ * (L / A), where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire, to find the cross-sectional area.

Assuming the wire has a uniform cross-sectional area, the formula can be rearranged as follows:

A = ρ * (L / R)

To find the current flowing through the wire, we can substitute the given values into Ohm's Law equation:

I = V / R

Now, let's calculate step-by-step.

1. Calculate the cross-sectional area (A):

Given:

• Length of wire (L) = 2 meters
• Resistance of wire (R) = 10 ohms

Assuming a resistivity (ρ) of the wire, which depends on the material, let's assume it is 1.72 x 10^-8 ohm meters.

A = ρ * (L / R) = (1.72 x 10^-8 ohm meters) * (2 meters / 10 ohms)

A = 3.44 x 10^-8 m^2

2. Calculate the current flowing through the wire (I):

Given:

• Voltage of battery (V) = 20 volts
• Resistance of wire (R) = 10 ohms

Using Ohm's Law equation:

I = V / R = (20 volts) / (10 ohms)

I = 2 amperes

Answer:

The current flowing through the wire is 2 amperes.