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3.1.7.     Direct Electrical Currents <CJ chap  20.8-20.15 >

3.1.7.1. Discussion

3.1.7.1.1.     Kirchhoff’s Laws:

3.1.7.1.1.1. Sum of currents entering a junction must equal the sum leaving the junction (node)

3.1.7.1.1.2. Sum of voltages across each element in any closed loop must be zero.

3.1.7.1.2.     Discuss:

3.1.7.1.2.1. Voltmeter

3.1.7.1.2.2. Galvanometer

3.1.7.1.2.3. Ammeter

3.1.7.1.3.     Discuss household wiring 110V and 220V, circuit breakers, …

3.1.7.2. Mathematical

3.1.7.2.1.     RCV circuit :  t = RC  is  the time constant of the circuit

3.1.7.2.1.1. If charging from a voltage V applied at t=0 then q(t) = Q₀(1-e^-t/RC)   and i(t) = (V/R)e^-t/RC 

3.1.7.2.1.1.1.     where Q₀ = CV 

3.1.7.2.1.2. If discharging a charged capacitor from t=0 then q(t) = Q₀e^-t/RC   and i(t) = I₀e^-t/RC

3.1.7.2.1.2.1.     where Q₀ = initial charge on the capacitor,  and I₀ = Q/RC

3.1.7.3. Advanced

3.1.7.3.1.     Solve the differential equations for the RCV circuit to derive the equations above

3.1.7.3.2.     Practice with complex circuit diagrams

3.1.7.3.3.     Take the resistance, r,  of  the battery into account in circuits

3.1.7.3.4.     Discuss the use of the Wheatstone bridge to measure an unknown resistor