The Biot number is a dimensionless number used in heat transfer to characterize the relative importance of conduction and convection in a system. It is defined as the ratio of the conductive resistance in the solid to the convective resistance in the fluid. In other words, the Biot number represents the relative contribution of conduction and convection in transferring heat between a solid and a fluid.

The Biot number can be calculated using the following formula:

Bi = hL / k

Where:
- Bi is the Biot number
- h is the convective heat transfer coefficient
- L is the characteristic length of the solid
- k is the thermal conductivity of the solid

Now, let's understand why the correct answer is option 'B' by examining the two terms in the Biot number equation.

1. Conductive resistance in the solid:
The conductive resistance in the solid refers to the resistance to heat transfer through conduction within the solid material. This resistance is determined by the thermal conductivity of the solid (k) and the characteristic length of the solid (L). A higher thermal conductivity or a larger characteristic length will result in a lower conductive resistance.

2. Convective resistance in the fluid:
The convective resistance in the fluid refers to the resistance to heat transfer through convection between the solid and the fluid. This resistance is determined by the convective heat transfer coefficient (h), which represents the ability of the fluid to transfer heat by convection. A higher convective heat transfer coefficient will result in a lower convective resistance.

Now, let's analyze the Biot number formula:

Bi = hL / k

- If the conductive resistance in the solid is greater than the convective resistance in the fluid, then the Biot number will be greater than 1. This indicates that conduction is dominant in transferring heat between the solid and the fluid.
- On the other hand, if the convective resistance in the fluid is greater than the conductive resistance in the solid, then the Biot number will be less than 1. This indicates that convection is dominant in transferring heat between the solid and the fluid.

Therefore, the correct answer is option 'B', which states that the Biot number signifies the ratio of conductive resistance in the solid to convective resistance in the fluid.