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.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the !! Resistor-Capacitor Circuits concept. If you need more !! Resistor-Capacitor Circuits practice, you can also practice !! Resistor-Capacitor Circuits practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Bennett's class at COD.