[Solved] the switch in the circuit shown below has been closed for a long time before it is opened at t \(= 0\). Find the voltage \(\mathrm { v } ( \mathrm { t } )\) across the capacitor for \(\mathrm { t } \geq 0\). Assume \(\mathrm { R } _ { 1 } = 2 \mathrm { k } \Omega , \mathrm { R } _ { 2 } = 3 \mathrm { k } \Omega , \mathrm { R } _ { 3 } = 1\) \(\mathrm { k } \Omega , \mathrm { L } = 125 \mathrm { mH } , \mathrm { C } = 0.05 \mu \mathrm { F } , \mathrm { V } _ { \mathrm { s } } = 5 \mathrm {~V}\). Residual Income: The income that remains after deducting all required expenses and cost of capital from operating income. Investment Centers: Segments within a company for which managers have responsibility over cost, revenue, and investment decisions. Cost Center: A business segment whose manager has control over cost but has no control over revenue or investments in operating assets. Responsibility Center: Any business segment whose manager has control over costs, revenues, or investments in operating assets.