A Hypothetical RC Circuit

R(a)=n=11an=1a1C(a)=n=01an=aa1R(a) = \sum_{n=1}^{\infty} \frac{1}{a^n} = \frac{1}{a-1} \qquad \qquad C(a) = \sum_{n=0}^{\infty} \frac{1}{a^n} = \frac{a}{a-1}

An RC ciruit consisting of a multitude of resistors (RR) in series followed by a multitude of capacitors (CC) in parallel is prepared such that the resistance and capacitance can be calculated with the series written above. At a=3a= 3, calculate the voltage (VV) of the capacitor when it has charged for t=2.5 secondst = 2.5 \space \text{seconds}, where the circuit's power supply voltage (VV_{\circ}) is 14 volts14 \space \text{volts}.

Round your answer to three significant figures.

Note: V(t)=V(1eN)V(t) = V_{\circ}(1-e^{N}) where N=-tRC N = \frac{\text{-t}}{\text{RC}} .

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