MP8-2: Problem 31.65

This one just needs a simple application of both Kirchhoff's loop law and junction law.

The first thing I did was figure out an equation for R_eq (R_ef) for the circuit using what we know about parallel resistors.

Using the junction law, you can easily find the current through the resistor by subtracting the ammeter's max from the current going into the circuit.

Then use the loop law to set V_A = V_R (V=IR) and solve for R_R.

Plugging that into your R_ef gives you a surprisingly pretty number if you use 2nd+ANS (for the full, non-rounded value) on your TI calculator. Or at least for these values, it did.

MP8-2: Problem 31.72

On page 986 of the text, you'll find the equation for the charge on a capacitor in an RC circuit as a function of time: Q = Q_0 * e^(-t/RC)

To figure out what time you'll have x% of Q_0, just set e^(-t/RC) to .x and solve for t.

The key to the second half is realizing that you'll have 1/sqrt(2) (about 70%) of Q_0 when the U_C is halved--

U_C = Q^2 / 2C
U_C /2 = (Q/sqrt(2))^2 / 2C
(page 952)

MP8-2: Problem 31.73

I used an equation that came up during the previous section: V = V_0 * e^(-t/RC)

Solve for R and input data from the point on the graph where t=2ms (2*10^-3).

MP8-2: An R-C Circuit

MP8-2: Problem 31.65 (spoiler)

MP8-1: Measuring the EMF and Internal Resistance of a Battery

MP8-1: Throw the Switch