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(7\%) Problem 12: Two capacitors are connected in a circuit in series as shown in the figure. The capacitances are \( C_{1}=15 \mu \mathrm{F} \), and \( C_{2}=13 \mu \mathrm{F} \). \( \triangleq 25 \% \) Part (a) Express the total capacitance \( C \) in terms of the two capacitances \( C_{1} \) and \( C_{2} \). \( C \) Hints: deduction per hint. Hints remaining: 1 Feedback: deduction per feedback. \( \Delta 25 \% \) Part (b) Calculate the numerical value of the total capacitance \( C \) in \( \mu \mathrm{F} \) ? \( \Delta 25 \% \) Part (c) If the battery carries a voltage of \( \Delta V \), express the total charge \( Q \) stored in the circuit in terms of capacitance \( C \) and voltage \( \Delta V \). \( \triangle 25 \% \) Part (d) Calculate the numerical value of \( Q \) in C given \( \Delta V=6.5 \mathrm{~V} \).