Question

Trapped on a deserted island, you salvage some copper wire and a generator to build a makeshift radio transmitter.

a) If you wrap the wire into an 8-turn coil of radius 3.8 cm and length 25cm, what is its inductance?
b) What capacitance do you need to make an RLC circuit with the coil that oscillates at the emergency
c) If you fashion the parallel-plate capacitor out of two aluminum squares, 5.0 cm on a side, what should be the separation distance between the two plates?

Answer 1

The inductance of the wire is 6.08 × 10-7 H, the capacitance needed for the RLC circuit is 4.17 × 10-12 F, and the separation distance between the plates of the parallel-plate capacitor is 1.51 × 10-3 m.

Step-by-step explanation:

(a) To find the inductance of the wire, we can use the formula:

L = (μ₀N²A) / l

Where L is the inductance, N is the number of turns, A is the area of the coil, and l is the length of the coil.

Plugging in the given values, L = (4π×10-7 × 8² × π × (0.038)2) / 0.25 = 6.08 × 10-7 H.

(b) To calculate the capacitance, we can use the formula:

C = 1 / (4π²f²L)

Where C is the capacitance and f is the frequency.

Plugging in the given values, C = 1 / (4π² × (100 × 106)² × 6.08 × 10-7) = 4.17 × 10-12 F.

(c) To find the separation distance between the plates of the parallel-plate capacitor, we can use the formula:

d = (2ε₀A) / C

Where d is the separation distance, ε₀ is the permittivity of free space, A is the area of the plates, and C is the capacitance.

Plugging in the given values, d = (2 × 8.85 × 10-12 × (0.05)2) / 4.17 × 10-12 = 1.51 × 10-3 m.