Equivalent resistance for 2 resistors in parallel:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}\frac{{\mathbf{R}}_{\mathbf{1}}{\mathbf{R}}_{\mathbf{2}}}{{\mathbf{R}}_{\mathbf{1}}\mathbf{+}{\mathbf{R}}_{\mathbf{2}}}}$

Equivalent resistance for resistors in series:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{n}}}}$

Ohm's law:

$\overline{){\mathit{i}}{\mathbf{=}}\frac{\mathbf{V}}{\mathbf{R}}}$

**A.**

R_{eq} = R_{1} + (R_{2})(R_{3})/(R_{2} + R_{3}) + R_{4}

R_{eq} = 36 + (36)(77)/(36 + 77) + 120 = 180.53Ω

From Ohm's law:

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R_{1} = R_{2} = 36 Ω, R_{3} = 77 Ω and R_{4} = 120 Ω. The capacitance is C = 67 μF and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.

A. The switch has been open for a long time when at time t = 0, the switch is closed. What is I_{4}(0), the magnitude of the current through the resistor R_{4} just after the switch is closed?

B. What is Q(∞), the charge on the capacitor after the switch has been closed for a very long time?

C. After the switch has been closed for a very long time, it is then opened. What is Q(t_{open}), the charge on the capacitor at a time t_{open} = 555 µs after the switch was opened?

D. What is I_{C,max}(closed), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is closed? A positive value for the current is defined to be in the direction of the arrow shown.

E. What is I_{C,max}(open), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is open? A positive value for the current is defined to be in the direction of the arrow shown.

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