Two wires of the same length and of the same materials have different diameters, d, and d2 (d,<d2) determine which wire has greater (i) conductivity? (ii) Conductance? 8. a. (i) State the fundamental laws of conservation of electric charges. (ii) What will happened to a

$$R' = \frac{4\rho (2L)}{\pi d^2} = 2 \left( \frac{4\rho L}{\pi d^2} \right) = 2R$$

The resistance will be $\boxed{2R}$.

ii) If its diameter is halved ($d' = d/2$):

$$R'' = \frac{4\rho L}{\pi (d/2)^2} = \frac{4\rho L}{\pi (d^2/4)} = 16 \left( \frac{4\rho L}{\pi d^2} \right) = 16R$$

The resistance will be $\boxed{16R}$.

Question 6:

The expression $\Omega = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$ represents the speed of light in vacuum ($c$).

$$c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \approx 3 \times 10^8 \text{ m/s}$$

The unit of speed is meters per second.

The expression evaluates to $\boxed{3 \times 10^8 \text{ m/s}}$.
Its unit is $\boxed{\text{meters per second (m/s)}}$.

Question 7:
Given: Two wires of the same length ($L$) and same material (resistivity $\rho$, conductivity $\sigma$). They have different diameters $d_1$ and $d_2$, with $d_1 < d_2$.

i) Which wire has greater conductivity?

Conductivity ($\sigma$) is an intrinsic property of the material. Since both wires are made of the same material, their conductivities are equal.
The wire with greater conductivity is $\boxed{\text{neither, they have the same conductivity}}$.

ii) Which wire has greater conductance?

Conductance ($G$) is the reciprocal of resistance ($R$), $G = \frac{1}{R} = \frac{A}{\rho L} = \frac{\pi d^2}{4\rho L}$.
Since $G \propto d^2$ and $d_1 < d_2$, the wire with the larger diameter ($d_2$) will have greater conductance.
The wire with greater conductance is $\boxed{\text{the wire with diameter } d_2}$.

Question 8:

a) (i) State the fundamental laws of conservation of electric charges.
The law of conservation of electric charge states that the net electric charge of an isolated system remains constant. Charge can neither be created nor destroyed, but it can be transferred from one object to another.

a) (ii) What will happened to a
This question is incomplete and cannot be answered.