A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit, if the current exceeds a predetermined value. Suppose that the material to be used in a fuse melts when the current density rises to 440 A/cm2. What diameter of cylindrical wire should be used to make a fuse that will limit the current to 0.46 A

3.64×10⁻² cm or 3.64×10⁻⁴ m

Explanation:

Current density = Current/cross sectional area.

δ = I/A Equation 1

Where δ = current density, I = current, A = cross sectional area of the wire.

make A the subject of the equation

A = I/δ Equation 2

Given: δ = 440 A/cm², I = 0.46 A

Substitute into equation 2

A = 0.46/440

A = 1.045×10⁻³ cm²

But,

A = πd²/4 Equation 2

Where d = diameter of the wire

make d the subject of the equation

d = √(4A/π) Equation 3

Given: A = 1.045×10⁻³ cm², π = 3.14

Substitute into equation 3

d = √(4×1.045×10⁻³/3.14)

d = √(1.33×10⁻³)

d = 0.0364 cm

d = 3.64×10⁻² cm or 3.64×10⁻⁴ m

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =