21.6 Dc circuits containing resistors and capacitors  (Page 5/9)

When is the potential difference across a capacitor an emf?

Regarding the units involved in the relationship $\tau =\text{RC}$ , verify that the units of resistance times capacitance are time, that is, $\Omega \cdot \mathrm{F}=\mathrm{s}$ .

The $\text{RC}$ time constant in heart defibrillation is crucial to limiting the time the current flows. If the capacitance in the defibrillation unit is fixed, how would you manipulate resistance in the circuit to adjust the $\text{RC}$ constant $\tau$ ? Would an adjustment of the applied voltage also be needed to ensure that the current delivered has an appropriate value?

When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the $\text{RC}$ constant of the circuit—it is not possible to measure time variations shorter than $\text{RC}$ . How would you manipulate $R$ and $C$ in the circuit to allow the necessary measurements?

Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in [link] , starting from $\text{t}=0$ . Draw the other for discharging a capacitor through a resistor, as in the circuit in [link] , starting at $\text{t}=0$ , with an initial charge $Q_0$ . Show at least two intervals of $\tau$ .

When charging a capacitor, as discussed in conjunction with [link] , how long does it take for the voltage on the capacitor to reach emf? Is this a problem?

When discharging a capacitor, as discussed in conjunction with [link] , how long does it take for the voltage on the capacitor to reach zero? Is this a problem?

Referring to [link] , draw a graph of potential difference across the resistor versus time, showing at least two intervals of $\tau$ . Also draw a graph of current versus time for this situation.