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In the RC circuit below the switch is connected to A for a long time such that the capacitor becomes fully charged. The switch is thrown to position B and the voltage across the capacitor recorded as a function of time. The voltage across the capacitor drops from its initial value of $V_C = 15 \:\text V$ down to $7.5 \:\text V$ in a time of $0.22 s$. The value of $R_1 = 50 \:\text k \Omega$ and $R_2 = 75 \:\text k \Omega$.

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Given the above information, what is the value of the capacitor?


$2.54 \: \mu \text F$


$1.76 \: \mu \text F$


$6.35 \: \mu \text F$


$4.23 \: \mu \text F$


$220 \: \mu \text F$

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