jubateee

2022-01-03

A capacitor that is charged to a potential of 12.0 V is then connected to a voltmeter that has an internal resistance of $3.40M\mathrm{\Omega}$. After a time of 4.00 s the voltmeter reads 3.0 V.

What are (a) the capacitance and (b) the time constant of the circuit?

esfloravaou

Beginner2022-01-04Added 43 answers

Step 1

Knowns

$R-C$ circuit, the charge on a discharging capacitor as a function of times is given by:

1)$q={Q}_{f}{e}^{-\frac{t}{RC}}$

Where$Q}_{f$ is the initial charge on the capasitor and $\tau =RC$ is the time constant of the circuit.

The capacitance C of a capacitor is the ratio of the chatge to the potential difference betwen its plates:

2)$C=\frac{Q}{V}$

Step 2

Given:

The initial voltage difference across the capacitor is${V}_{0}=12.0V$ , the internal resistance of the valtmater is $R=3.40\times {10}^{6}\mathrm{\Omega}$ and after time $t=4.00s$

Step 3

Calculations

Solving equation (2) for V, we get:

$V=\frac{Q}{C}$

So, by dividing equation (1) by C, we get the voltage across a discharging capacitor as a function of ti,e:

3)$V={V}_{0}{e}^{-\frac{t}{RC}}$

Where$V}_{0}=\frac{{Q}_{f}}{C$ is the initial voltage diffence.

When we connent the capacitor to the voltameter, the capacitor discharges its charge in the internal resistance of the voltameter.

And from Kirchoffs

Knowns

1)

Where

The capacitance C of a capacitor is the ratio of the chatge to the potential difference betwen its plates:

2)

Step 2

Given:

The initial voltage difference across the capacitor is

Step 3

Calculations

Solving equation (2) for V, we get:

So, by dividing equation (1) by C, we get the voltage across a discharging capacitor as a function of ti,e:

3)

Where

When we connent the capacitor to the voltameter, the capacitor discharges its charge in the internal resistance of the voltameter.

And from Kirchoffs

Orlando Paz

Beginner2022-01-05Added 42 answers

Step 1

This is the discharge of electricity through a resistor, so the decrease in voltage and charge is exponential

$V={V}_{0}{e}^{-\frac{t}{RC}}$

$\mathrm{ln}\frac{V}{{V}_{0}}=-\frac{t}{RC}$

$RC=-\frac{t}{\mathrm{ln}\left(\frac{V}{{V}_{0}}\right)}=\frac{t}{\mathrm{ln}\left(\frac{{V}_{0}}{V}\right)}$

$RC=\frac{4}{\mathrm{ln}\left(\frac{12}{3}\right)}=2.885$ seconds

Thats

At the beginning of an environmental study, ad forest covered an area of $1500k{m}^{2}$.Since then, this area has decreased by 4.25% each year.Let t be the number of years since the start of the study.Let y be the area that the forest covers in $k{m}^{2}$.

Write an exponential function showing relationship between y and t.Some friends tell you that they paid $25,000 down on a new house and are to pay $525 per month for 30 years. If interest is 7.8% compounded monthly, what was the selling price of the house? How much interest will they pay in 30 years?

t e^-4t sin3t

Find all whole number solutions of the congruence equation.

3x ≡ 8 mod 11Use a direct proof to show that the product of two rational numbers is rational.

Y=2(x-) (x+1)

what is vertex

axis of symmetry

x-intercept(s)

y-intercept

Stairs- Each step of a set of stairs has a tread depth of 11.5 inches and a riser height of 6.5 inches. What is the slope of the set of stairs?

A ball of mass 5 kg is attached to a string of length 10 cm, forming a pendulum. If the string is raised horizontally as shown and released from point A, then what is the v

assume that the random variable Xand Y have the joint pdf f(x,y)=1/2x^3

5=20 mod 4 true or false answer

5x−4y=

- $\text{\hspace{0.17em}}\text{\hspace{0.17em}}-12$−12

Pets Plus and Pet Planet are having a sale on the same aquarium. At Pets Plus the aquarium is on sale for 30% off the original price and at Pet Planet it is discounted by 25%.

**Store****Original Price****of Aquarium ($)**Pets Plus 118 Pet Planet 110 If the sales tax rate is 8%, which store has the lower sale price?

, 1 of 1.Select ChoicePets PlusPet Planet has the lower sale price.

**Part B**Fill in the blank question.

How much will you save by buying the aquarium at the store with the lower sale price? Round to the nearest cent.

$

Prove that if x is and irrational number and x>0 then route over x is also irrational

A small object has charge Q. Charge q is removed from it and placed on a second small object. The two objects are placed 1 m apart. For the force that each object exerts on the other to be a maximum. q should be: A. 2Q B. Q C. Q/2 D. Q/4 E. 0