1. PHYS 219 Recitation
Kevin Ralphs
Week 4

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

3. 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

4. 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.

5. 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

6. 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

7. 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 )