Given Information:
Diameter of spherical cell = 0.040 mm
thickness = L = 9 nm
Resistivity = ρ = 3.6×10⁷ Ω⋅m
Dielectric constant = k = 9.0
Required Information:
time constant = τ = ?
Answer:
time constant = 2.87×10⁻³ seconds
Explanation:
The time constant is given by
τ = RC
Where R is the resistance and C is the capacitance.
We know that resistivity of of any material is given by
ρ = RA/L
R = ρL/A
Where area of spherical cell is given by
A = 4πr²
A = 4π(d/2)²
A = 4π(0.040×10⁻³/2)²
A = 5.026×10⁻⁹ m²
The resistance becomes
R = (3.6×10⁷*9×10⁻⁹)/5.026×10⁻⁹
R = 6.45×10⁷ Ω
The capacitance of the cell membrane is given by
C = kεoA/L
Where k = 9 is the dielectric constant and εo = 8.854×10⁻¹² F/m
C = (9*8.854×10⁻¹²*5.026×10⁻⁹)/9×10⁻⁹
C = 44.5 pF
C = 44.5×10⁻¹² F
Therefore, the time constant is
τ = RC
τ = 6.45×10⁷*44.5×10⁻¹²
τ = 2.87×10⁻³ seconds
Answer:
0.166 rad/s
Explanation:
See attachment for calculations
Answer:
78 km/h
Explanation:
If I normally drive a 12 hour trip at an average speed of 100 km/h, my destination has a total distance of:
- 100 km/h · 12 h = 1,200 km
Today, I drive the first 2/3 of the distance at 116 km/h. Let's first calculate what 2/3 of the normal distance is.
I've driven 800 km already. I need to drive 400 km more to reach my final destination. I need to figure out my average speed during this last 1/3 of the distance.
To do this, I first need to calculate how much time I spent driving 116 km/h for the past 800 km.
- 116 km/1 h = 800 km/? h
- 800 = 116 · ?
- ? = 800/116
- ? = 6.89655172
I spent 6.89655172 hours driving during the first 2/3 of the distance.
Now, I need to subtract this value from 12 hours to find the remaining time I have left.
- 12 h - 6.89655172 h = 5.10344828 h
Using this remaining time and my remaining distance, I can calculate my average speed.
- ? km/1 hr = 400 km/5.10344828 h
- 5.10344828 · ? = 400
- ? = 400/5.10344828
- ? = 78.3783783148
My average speed during the last third of the distance is around 78 km/h.
Answer:
1 km
Explanation:
Bob travels at one km/h and it takes him one hour to get there.
