Question

Suppose the switch is closed at t = 0 s. How much time passes until the charge on the capacitor is 0.00099 C? Hint1: Use your answers to the previous questions to write the expression for the charge on the capacitor as a function of time, which you can find in the book Hint2: The inverse operation of exponentiation is taking the natural logarithm. In other words, In(e) = x

Answer 1

The time until the charge on the capacitor is 0.00099 C in an RC circuit is determined by the formula q(t) = Q(1 - e^{-t/RC}) and rearranging for t, but specific values for R, C, and emf are needed to perform the calculation.

Step-by-step explanation:

To determine how much time passes until the charge on the capacitor is 0.00099 C, we use the formula for the charging of a capacitor in an RC circuit, which is q(t) = Q(1 - e^{-t/RC}), where q(t) is the charge on the capacitor at time t, Q is the maximum charge, and RC is the time constant T. To find the time t, we rearrange the formula to solve for t:

• q(t)/Q = 1 - e^{-t/RC}
• e^{-t/RC} = 1 - q(t)/Q
• -t/RC = ln(1 - q(t)/Q)
• t = -RC ln(1 - q(t)/Q)

Plugging the given charge q(t) = 0.00099 C into the equation, we would solve it to get the time t. The specific values for R (resistance) and C (capacitance) are needed, along with the knowledge that the initial charge is zero and the maximum charge Q is Cε, to calculate the precise time. However, as these values are not provided, the calculation cannot be completed without them.