Circuit 1:

• The total resistance is 30
• R₄ = 10
• V₁ = 5
• V₂ = 8
• V₃ = 7

Determine values for the remaining R's and what the total current I is.

Well begin by writing down all you know:

• R₁ + R₂ + R₃ must equal 20.
• notice that V₁ + V₂ + V₃ equals 20
• in a series circuit the current is every where the same but the voltages obviously vary. Apply ohms law to the first three resistors to get V (which is 20) = R (which is 20) * I
• I must be 1.
• and therefore R₁ = 5; R₂=8; R₃=7

Circuit 2:

• Determine I₁,I₂,I₃
• Determine the total R

First you need to determine total R:

1/R = 1/2 + 1/3 + 1/6 = 1/1; R =1

Apply ohms law to total circuit: V = 12 = R(=1) * I; so I = 12 Now apply ohms law to each resistor:

I₁ = V/R₁ = 12/2 = 6
I₂ = V/R₂ = 12/3 = 4
I₃ = V/R₃ = 12/6 = 2

Circuit 3:

• Enter in values for I₁ (top resistor) and I₂ (bottom resistor). Total incoming current is 3 amps.

Voltage is constant in a parallel circuit. Therefore, high resistance means lower current flow through that resistor (this should be intuitive).

Two ways to work this out:

Anal way:

What is total resistance:

1/R = 1/8 + 1/4 = 3/8; R = 8/3

I = 3

V = I*R = 3*8/3 so V = 8

Top resistor: V=R*I; 8=8*I; I = 1

Bottom resistor: V=R*I 8 =4*I; I = 2

Better way;

Notice the ratio of the resistors is 2:1; therefore the ratio of the currents is 1:2

Circuit 4:

• The value for all Resistors is the same and is equal t0 2 ohms. Determine values for V₁ and V₂

  The resistance of the parallel part (at location V₂) is: 1/R= 1/2+1/2 =1; R=1

  the resistance at location V₁ is obviously = 2 so the total resistance is 1 +2 = 3 ohms. Total current is then 12/3 = 4 amps.

  Too find the voltage drops, now treat this as a serial circuit with equivalent resistance of 2+1 ohms.

  So V₁ = 2x4 = 8 Volts

  V₂ = 1x4 = 4 Volts

  Note that it doesn't matter what the value of R actually is, the same values of V₁ and V₂ are always found.

  Ratio way

  In series circuit I is constant; V=RI; If R goes up; V goes up; Ratio of R's is 2:1 therefore ratio of V's is 2:1 or 8 volts at position 1 and 4 volts at position 2.

• Determine the total resistance for the configurations shown in I, II, and III
  • Circuit I: Parallel + series. The bottom leg total resistance is 4 + 4 = 8. The total resistance in the parallel circuit is then:

    1/R = 1/4 + 1/8 = 3/8 so R = 8/3

  • Circuit II: total resistance is 4 + what is in the parallel part. Parallel part: 1/R = 1/4 + 1/4 = 1/2 so R = 2 so total is 4+2 =6

  • Circuit III: Straight parallel circuit:

    1/R = 1/4 + 1/4 + 1/4 = 3/4 so R = 4/3