PHYS 219 Recitation Kevin Ralphs Week 4

Overview HW Questions Kirchoff’s Rules Capacitors, Current, Time

Kirchoff’s Rules Loop Rule Node Rule Based on conservation of energy 𝐿𝑜𝑜𝑝 Δ 𝑉 𝑖 =0 Node Rule Based on conservation of charge 𝐼 𝑗 =0

Kirchoff’s Rules General Procedure: Choose loops so that every branch is covered by at least one loop Choose current directions in each branch – this does not have to correspond to the direction of your loop Write down each loop/node equation and solve using method of your choice. You need as many independent equations as you have currents to solve.

Kirchoff’s Rules Voltage Source The most common errors in applying Kirchoff’s rules are sign errors Voltage Source Resistor (Black arrows denote a positive change in voltage; red negative) Current

Capacitors, Current, Time You will be responsible for understanding how a capacitor behaves at various times during charging/discharging The end points are simple If uncharged, a capacitor acts as a short If charged, a capacitor acts as an open The words “after a long time” or similar mean it has gone from charged to uncharged or vice versa

Capacitors, Current, Time In between it is governed by equations Note: 𝑄 𝑜 , 𝑉 𝑜 , 𝑅 vary depending on whether you are charging/discharging and what resistors you are charging/discharging through Charging 𝑄= 𝑄 𝑜 (1− 𝑒 − 𝑡 𝜏 ) 𝐼= 𝐼 𝑜 𝑒 − 𝑡 𝜏 Discharging 𝑄= 𝑄 𝑜 𝑒 − 𝑡 𝜏 𝐼= 𝐼 𝑜 (1−𝑒 − 𝑡 𝜏 )