Analyzing a Parallel Circuit Water analogy Think of

Analyzing a Parallel Circuit

Water analogy • Think of a parallel circuit as a waterfall with several paths on which water can flow down – Some paths might have heavy flow – Some might have lighter flow – SUM of paths will equal the total flow of water over the falls – Regardless of path, the height drop is the same – Water in a pump analogy

Current Image of circuit with gravity • Current will depend on individual resistor across which it is travelling • When we additional paths for the current, there is more current in the circuit

Resistance • To find equivalent resistance in a parallel circuit: • Equivalent resistance will be LESS than any single resistor!! Hmm…those fractions look scary—but they AREN’T!! Be ready to work with them!!

Example: Calculate Rtotal

LCD! Add fractions and simplify Cross multiply

Summary: • For parallel: – Total resistance – Voltage drop across each branch will be the same – Current across each branch will be different, depending on the resistance – Total current = sum of current across the branches

Break for independent practice

Steps: • Find total resistance • Find total current • Find current at each branch

Example #1: Rtotal = 4Ω

Example #1: R 1 = 12Ω

Example #1: R 2= 6Ω Check: 1 A + 2 A = 3 A YES!

Example:

Step 1: Total resistance

Step 2: Determine I of the circuit V=IR 90 V = (I)(10Ω) 9 A = I

Step 3: Determine I at each resistor • Resistor 1 = 60Ω • V=IR • 90 V=(I)(60 Ω) • 1. 5 A = I 1

Step 3: Determine I at each resistor • Resistor 2 = 20Ω • V=IR • 90 V=(I)(20 Ω) • 4. 5 A = I 2

Step 3: Determine I at each resistor • Resistor 3 = 30Ω • V=IR • 90 V=(I)(30 Ω) • 3 A = I 3

Check! • TOTAL Current should be sum of each branch: 1. 5 A + 4. 5 A + 3 A = 10 A YES!

Currents Voltage Series Itotal=I 1=I 2=I 3… Vtotal=V 1+V 2+V 3… Resistance Rtotal = R 1+R 2+R 3 … Parallel Itotal=I 1+I 2+I 3… Vtotal=V 1=V 2=V 3… (across branches)