Two copper wires have equal cross-sectional areas and lengths of 2.4m and 1.3m, respectively.

What is the ratio of the current in the shorter wire to that in the longer one if they are connected to the same power supply?
I1.3/I2.4 =

Resistance of wire is proportional to length in this case (same area for both wires).

For equal voltages on both wires, current is inversely proportional to resistance. Current is therefore also inversely proportional to length.

To determine the ratio of current in the shorter wire to that in the longer wire, we can make use of Ohm's Law and the relationship between current and resistance.

First, let's assume that the resistivity of both copper wires is the same. This is a reasonable assumption because the wires have equal cross-sectional areas.

We know that resistance (R) is given by:

R = resistivity (ρ) * length (L) / cross-sectional area (A)

Since the resistivity and cross-sectional area are the same for both wires, the resistance of each wire is inversely proportional to its length.

Therefore, we can represent the resistance of the shorter wire (R1.3) and the longer wire (R2.4) in the following way:

R1.3 = constant / 1.3
R2.4 = constant / 2.4

Now, let's consider the relationship between current (I), voltage (V), and resistance (R), as given by Ohm's Law:

V = I * R

Since both wires are connected to the same power supply, the voltage across them is the same. This means we can equate the voltage in both equations.

I1.3 * R1.3 = I2.4 * R2.4

Substituting the expressions for R1.3 and R2.4:

I1.3 * (constant / 1.3) = I2.4 * (constant / 2.4)

The constants and the resistivity cancel out:

I1.3 / 1.3 = I2.4 / 2.4

Simplifying, we find:

I1.3 / I2.4 = 2.4 / 1.3

Therefore, the ratio of the current in the shorter wire to that in the longer wire is approximately 1.846.

To find the ratio of the current in the shorter wire to the longer wire, we can use Ohm's Law, which states that the current (I) flowing through a conductor is equal to the voltage (V) applied across it divided by its resistance (R).

Since both wires are connected to the same power supply, they will have the same voltage applied across them. Therefore, the voltage can be canceled out when finding the ratio of currents.

The resistance of a wire is given by the formula:
R = resistivity (ρ) * length (L) / cross-sectional area (A)

Since the cross-sectional areas of the two wires are equal, we can ignore the A.

Let's denote the resistance of the 2.4-meter wire as R1 and the resistance of the 1.3-meter wire as R2.

Now, we can set up the following equation based on Ohm's Law:
I1 / I2 = (V / R1) / (V / R2)

Simplifying the equation, we can cancel out the V:
I1 / I2 = R2 / R1

We are given the lengths of the wires, so we can calculate their resistance since resistivity is a property of the material.

Let's assume the resistivity of copper is 1.68 × 10^-8 Ω⋅m.

Calculating the resistance for each wire:
R1 = 1.68 × 10^-8 Ω⋅m * 2.4 m
R2 = 1.68 × 10^-8 Ω⋅m * 1.3 m

Now we can substitute these values into the equation:
I1 / I2 = (1.68 × 10^-8 Ω⋅m * 1.3 m) / (1.68 × 10^-8 Ω⋅m * 2.4 m)

Simplifying further:
I1 / I2 = (1.68 × 10^-8 * 1.3) / (1.68 × 10^-8 * 2.4)

Finally, we can cancel out the resistivity:
I1 / I2 = 1.3 / 2.4

Therefore, the ratio of the current in the shorter wire to the longer one is 1.3 / 2.4.