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Analyzing Brightness Changes in an RC Circuit with Varying Resistors

This content examines the dynamics of a circuit containing five equal resistance light bulbs, focusing on the impact of replacing bulb 2 with a lower resistance bulb on bulb 1's brightness. We explore theoretical calculations and circuit diagrams to aid understanding. Additionally, we cover the principles of discharging and charging RC circuits, including current flow and the exponential decay of charge in capacitors. This material is presented as part of Oregon State University's PH 213 Class #18, inviting students to deepen their grasp of electrical principles and calculations.

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Analyzing Brightness Changes in an RC Circuit with Varying Resistors

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  1. Consider the following circuit, initially with five equal resistance light bulbs. If bulb 2 is replaced with a bulb of lower resistance, what will happen to the brightness of bulb 1? • Increase • Decrease • Stay the same • Sounds complicated – we should calculate it Oregon State University PH 213, Class #18

  2. Which of these diagrams represent the same circuit? • a and b • b and c • a and c • a, b, and d • a, b, and c Oregon State University PH 213, Class #18

  3. A discharging RC circuit Charge on capacitor: Q = CDVC Current flowing from capacitor: I = –dQ/dt Kirchhoff’s loop rule: DVC – IR = 0 Q/C – IR = 0 Q/C + RdQ/dt = 0 Q = –RC(dQ/dt) Q(t) = Q0e–t/(RC) Exponential decay! So.. I(t) = ?DVC (t) = ? Oregon State University PH 213, Class #18

  4. A discharging RC circuit Oregon State University PH 213, Class #18

  5. What value resistor will discharge a 1.0 μF capacitor to 10% of its initial charge in 2.0 ms? Oregon State University PH 213, Class #18

  6. A charging RC circuit Battery, R, and C; current starts from I = 0 at time t = 0. Q = CDVC on a capacitor, current I = dQ/dt Kirchhoff’s loop rule: DVb – Q/C – IR = 0 DVb – Q/C – (dQ/dt)R = 0 Qmax/C – Q/C – (dQ/dt)R = 0 Q = Qmax(1 – e–t/(RC)), where Qmax = CDVb So.. I(t) = ?DVC (t) = ? Oregon State University PH 213, Class #18

  7. A charging RC circuit Oregon State University PH 213, Class #18

  8. The switch has been closed for a very long time. Before the switch is opened, what is the current through the 10 Ω resistor? • maximum • positive • zero • Sounds complicated – we should calculate it Oregon State University PH 213, Class #18

  9. The switch has been closed for a very long time. At t = 0 s the switch is opened. Immediately after the switch opens, what is the current through the 10 Ω resistor? • maximum • positive • zero • Sounds complicated – we should calculate it Oregon State University PH 213, Class #18

  10. Oregon State University PH 213, Class #18

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