(Solved): Problem 3: A bank of batteries, total emf \( \varepsilon=4.5 \mathrm{~V} \), is in a circuit with ...

Problem 3: A bank of batteries, total emf \( \varepsilon=4.5 \mathrm{~V} \), is in a circuit with resistor \( R=180 \mathrm{k} \Omega \), capacitor \( C=680 \mathrm{nF} \), and two-pole switch \( S \) as shown. The switch is initially set to point a so that the batteries, resistor, and capacitor are in series. The switched is left in this position for a sufficiently long time so that the capacitor is fully charged. Randomized Variables \[ \begin{array}{l} \varepsilon=4.5 \mathrm{~V} \\ R=180 \mathrm{k} \Omega \\ C=680 \mathrm{nF} \end{array} \] \( \triangle 17 \% \) Part (a) Calculate the maximum charge \( Q \) on the capacitor (in coulombs). \( Q= \) Hints: deduction per hint. Hints remaining: 2 Feedback: deduction per feedback. Part (b) The switch is moved from point \( a \), but not connected to point \( b \). What will happen to the voltage across the capacitor? The voltage will not change \( \checkmark \) Correct! \( \triangle \)...o Part (c) The switch is now (at \( t=0 \) ) moved to point \( b \). Determine the current through resistor \( R \) (in amperes) the instant the switch is closed. You may assume the direction of this current is positive. i i Part (d) Determine an expression for the voltage across the capacitor as a function of time, with the switch at position \( b \), in terms of the emf \( \varepsilon \). \( V(t)=\varepsilon \mathrm{e}^{-t}( \) R C \( ) \quad \checkmark \) Correct! @ Part (e) Calculate the time (in seconds), after contact is made by the switch at position \( b \), that it will take the capacitor to discharge halfway. \( \triangleq \quad \) Part (f) Calculate the current through the resistor (in amperes) at time \( \mathrm{t}=75 \mathrm{~ms} \) after the switch is connected to point \( b \).