In the circuit below the capacitor is initially uncharged. At time $t=0 \:\text s$ the switch is thrown to position A and the capacitor begins to charge. After 7 minutes the switch is moved quickly to position B. The circuit parameters are: the battery voltage $\Delta V = 15 \:\text V$, $R = 60 \:\text k \Omega$, $C= 0.01 \:\text {F}$.

What is the voltage across the capacitor 3 minutes after the switch is moved to B?