A rectangular conducting homogeneous (which means the material is the same throughout) block has dimensions 1cm×2cm×3cm . A voltage V is applied between all opposite faces of the block and the corresponding currents were recorded. What is the maximum current measured in Amps if the minimum current recorded is 1mA.
To find the maximum current measured in Amps, we can make use of Ohm's law and the concept of resistance.
First, we need to understand the relationship between current, voltage, and resistance. Ohm's law states that the current passing through a conductor is directly proportional to the voltage applied across it and inversely proportional to its resistance. Mathematically, Ohm's law can be expressed as:
I = V / R
Where:
I is the current (in Amperes),
V is the voltage (in Volts), and
R is the resistance (in Ohms).
In this case, the conducting block is rectangular with dimensions 1cm × 2cm × 3cm. Since the material is homogeneous, we can consider its resistance to be constant.
To find the resistance of the block, we can use the formula:
R = ρ * (L / A)
Where:
R is the resistance (in Ohms),
ρ (rho) is the resistivity of the material (in Ohm-meters),
L is the length of the conducting path (in meters), and
A is the cross-sectional area of the conducting path (in square meters).
Since we have the dimensions of the block in centimeters, we need to convert them to meters:
Length (L) = 3 cm = 0.03 m
Width (W) = 2 cm = 0.02 m
Height (H) = 1 cm = 0.01 m
The cross-sectional area (A) can be calculated as:
A = W * H = (0.02 m) * (0.01 m) = 0.0002 m²
The resistivity ρ is a material property and can be found from reference sources.
Once we have the value of ρ, we can calculate the resistance (R) of the conducting block.
Now, let's consider the maximum and minimum currents recorded. The minimum current recorded is given as 1 mA (milliampere), which is 0.001 A.
To find the maximum current, we need to rearrange Ohm's law:
I = V / R
Rearranging for V, we get:
V = I * R
Substituting the minimum current and resistance values, we can find the corresponding voltage:
V = (0.001 A) * (R)
Finally, to find the maximum current, we need to find the voltage required for the maximum current measurement. Once we have the voltage value, we can substitute it back into Ohm's law to determine the maximum current.
Please provide the value of the resistivity ρ to proceed with the calculation and find the maximum current measured in Amps.