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(7\%) Problem 13: Two capacitors are in a circuit, connected in parallel as shown in the figure. The capacitances are \( C_{1}=8.2 \mu \mathrm{F} \) and \( C_{2}=7.4 \mu \mathrm{F} \). The battery carries a voltage of \( \Delta V=9.8 \mathrm{~V} \). \( \triangle 25 \% \) 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: Feedback: deduction per feedback. A 25\% Part (b) Calculate the numerical value of the total capacitance \( C \) in \( \mu \mathrm{F} \). \( \triangle 25 \% \) Part (c) Express the total charge on both of the capacitors \( Q \) in terms of capacitance \( C \) and the potential difference \( \Delta V \). \( \triangleq 25 \% \) Part (d) Calculate the numerical value of \( Q \) in \( \mu \mathrm{C} \).

13. .a) Two capacitors ar