Circuit Diagram Equivalent Resistance Quiz

Circuit Diagram 1

• A 30 Ω resistor is connected in series with a 20 Ω resistor.
• The combination of the 30 Ω and 20 Ω resistors is then connected in parallel with a 60 Ω resistor
• To find the equivalent resistance at terminals a-b, we first calculate the series combination of the 30 Ω and 20 Ω resistors.
• The total resistance of the series combination is 30 Ω + 20 Ω = 50 Ω.
• This 50 Ω resistor is then in parallel with the 60 Ω resistor.
• The equivalent resistance of a parallel combination can be calculated using the formula: 1/R_eq = 1/R_1 + 1/R_2.
• In this case, 1/R_eq = 1/50 + 1/60.
• Solving for R_eq gives us approximately 27.27 Ω.

Circuit Diagram 2

• A 30 Ω resistor is connected in parallel with a 60 Ω resistor.
• A 40 Ω resistor is connected in parallel with an 80 Ω resistor.
• The equivalent resistance of the parallel combination of the 30 Ω and 60 Ω resistors can be calculated using the formula: 1/R_eq = 1/R_1 + 1/R_2.
• In this case, 1/R_eq = 1/30 + 1/60.
• Solving for R_eq gives us 20 Ω.
• The equivalent resistance of the parallel combination of the 40 Ω and 80 Ω resistors can be calculated using the formula: 1/R_eq = 1/R_1 + 1/R_2.
• In this case, 1/R_eq = 1/40 + 1/80.
• Solving for R_eq gives us 26.67 Ω.
• The 20 Ω resistor is then connected in series with a 10 Ω resistor and a 50 Ω resistor.
• The 26.67 Ω resistor is then connected in series with the combination of the 20 Ω, 10 Ω and 50 Ω.
• The total resistance of the series combination is 20 Ω + 10 Ω + 50 Ω + 26.67 Ω = 106.67 Ω.
• Therefore, the equivalent resistance at terminals a-b is 106.67 Ω.