A 2.0 micro farad capacitor in a circuit in series with a resistor of .0 MOhms is charged witha 6.0V battery. How long would it take to charge to 3/4 of its maximum voltage?

that was 1.0 MOhms

RC time constant: 2E-6*1E=6=2seconds

V=Vo (1-e^(-t/RC))
with a little math,
.25=e^-t/rc

take the ln of each side..

-ln(.25) * RC=t
-2ln(.25)=t
t=2.77 seconds check that

To find out how long it takes for the capacitor to charge to 3/4 of its maximum voltage, we need to understand the charging process of a capacitor in an RC circuit.

In an RC circuit, the voltage across the capacitor (Vc) increases over time according to the equation:

Vc = V_max * (1 - e^(-t / RC))

Where:
- Vc is the voltage across the capacitor at a given time (in this case, 3/4 of the maximum voltage)
- V_max is the maximum voltage that the capacitor can reach when fully charged (which is the battery voltage, 6.0V in this case)
- t is the time in seconds
- R is the resistance in ohms
- C is the capacitance in farads

We know the values for all the variables except for t, which is what we are trying to find. Let's plug in the values and solve for t:

Vc = 3/4 * V_max = 3/4 * 6.0V = 4.5V
R = 0.0 MOhms = 0.0 * 10^6 Ω = 0 Ω (resistance is effectively zero)
C = 2.0 μF = 2.0 * 10^-6 F

4.5V = 6.0V * (1 - e^(-t / (0 * 2.0 * 10^-6 F)))

Since the resistance is zero (a short circuit), the exponential term becomes 1:

4.5V = 6.0V * (1 - e^0)

Simplifying further:

4.5V = 6.0V * (1 - 1)

4.5V = 6.0V * 0

Therefore, the time required for the capacitor to reach 3/4 of its maximum voltage is instantaneous in this case since the resistance is zero.

To find the time it takes for a capacitor to charge to a specific voltage, we need to use the RC time constant formula, which calculates the time it takes for a capacitor to charge or discharge to approximately 63.2% of its maximum voltage.

The RC time constant formula is given by:

τ = R * C

where:
τ is the time constant (in seconds)
R is the resistance (in ohms)
C is the capacitance (in farads)

In this case, the capacitor has a capacitance of 2.0 micro farads (2.0 x 10^(-6) F) and is in series with a resistor of 0.0 megaohms (0.0 x 10^6 Ω). We can convert these values to farads and ohms respectively:

C = 2.0 x 10^(-6) F
R = 0.0 x 10^6 Ω = 0 Ω

As the resistance is zero, the RC time constant becomes zero, which means that the capacitor will charge instantaneously to its maximum voltage. Therefore, we cannot use the RC time constant formula to find the time it takes for the capacitor to charge to 3/4 of its maximum voltage.

Instead, we need to make an assumption about the resistor value or recalculate the problem with a non-zero resistor value in order to calculate the charging time.