Question

Suppose you have a 2.25 cm diameter rod of pure silicon that is 25 cm long.

What current, in amperes, flows through it when a potential difference of 0.75 × 103 V is applied between its ends? These rods are often used in experiments, such as the Large Hadron Collider in France/Switzerland to detect high-energy particles, and have a very high resistivity of 2300 Ω⋅m.

Answer 1

To find the current flowing through the silicon rod, we can use Ohm's Law, which states that the current (I) is equal to the potential difference (V) divided by the resistance (R):

I = V / R

First, let's calculate the resistance of the silicon rod using its resistivity (ρ), length (L), and cross-sectional area (A):

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

The diameter of the rod is given as 2.25 cm, so the radius (r) can be calculated as half of the diameter:

r = 2.25 cm / 2 = 1.125 cm = 0.01125 m

The cross-sectional area (A) of the rod can be calculated using the formula:

A = π * r^2
Substituting the values into the equation:

A = π * (0.01125 m)^2

Next, we calculate the resistance:

R = 2300 Ω⋅m * (25 cm / (π * (0.01125 m)^2))

Now, we can calculate the current (I):

I = 0.75 × 10^3 V / R

Substituting the value of R, we can solve for I:

I = 0.75 × 10^3 V / (2300 Ω⋅m * (25 cm / (π * (0.01125 m)^2)))

Calculating the above expression will give us the current flowing through the silicon rod in amperes.