Question 1

Series versus parallel path count How does a parallel circuit differ from a series circuit with respect to the number of available paths for current flow?

Accepted Answer

Introduction / Context: Distinguishing series and parallel arrangements is a cornerstone skill in circuit analysis and troubleshooting. Many real circuits mix both, so being able to identify how current flows is essential. Given Data / Assumptions: Ideal wires and sources; steady DC conditions. Series means components share the same current; parallel means components share the same voltage. Concept / Approach: In a series connection, the current has exactly one path and is the same through each component. In a parallel connection, multiple independent paths exist between the same two nodes; the current splits among branches based on their impedances while the voltage across each branch remains the same. Step-by-Step Solution: Define series: single current path through all components.Define parallel: multiple paths between common nodes; currents add at the node.Select the description that matches parallel: more than one path for current flow. Verification / Alternative check: Apply KCL at a junction in a parallel network: the sum of branch currents equals the source current, confirming multiple paths. Why Other Options Are Wrong: No path: describes an open circuit, not a parallel network. Fewer paths: relative wording is ambiguous and not a defining property. One path: defines a series circuit, not a parallel circuit. Common Pitfalls: Assuming current is the same in parallel branches; that is the series rule. In parallel, voltage is the same and current divides according to branch impedance. Final Answer: More than one path for current flow

Question 2

Compute the equivalent resistance for resistors in parallel What is the total resistance RT of 12 kΩ, 4 kΩ, and 3 kΩ connected in parallel?

Accepted Answer

Introduction / Context: Calculating equivalent resistance of parallel resistors is a routine but critical task in electronics. It determines load seen by sources, affects current sharing, and impacts power dissipation and noise performance in analog designs. Given Data / Assumptions: Three resistors: R1 = 12 kΩ, R2 = 4 kΩ, R3 = 3 kΩ. All three are connected in parallel across the same two nodes. DC conditions and ideal components. Concept / Approach: For resistors in parallel, conductances add: 1/RT = 1/R1 + 1/R2 + 1/R3. After summing the reciprocals, invert to get RT. Using kilohm units throughout avoids unit mistakes. Step-by-Step Solution: Compute reciprocals: 1/R1 = 1/12 kΩ = 0.08333 kΩ^-1.Compute 1/R2 = 1/4 kΩ = 0.25 kΩ^-1; 1/R3 = 1/3 kΩ ≈ 0.33333 kΩ^-1.Sum: 0.08333 + 0.25 + 0.33333 ≈ 0.66666 kΩ^-1.Invert: RT = 1 / 0.66666 ≈ 1.5 kΩ. Verification / Alternative check: Use pairwise combination: combine 3 kΩ || 6 kΩ (since 12 kΩ || 4 kΩ = 3 kΩ) gives 3 kΩ || 3 kΩ = 1.5 kΩ. Both methods agree. Why Other Options Are Wrong: 2 kΩ: corresponds to 1/RT = 0.5 kΩ^-1, which is smaller than the actual sum of conductances. 6.3 kΩ or 19 kΩ: larger than the smallest branch resistance; a parallel equivalent can never exceed the smallest resistor. Common Pitfalls: Failing to keep consistent units (ohms vs kilohms) and forgetting that the equivalent of parallel resistors is always less than the smallest individual resistor. Final Answer: 1.5 kΩ

Question 3

If a branch opens in a parallel circuit, the current in the remaining parallel paths will change.

Accepted Answer

True

Question 4

The largest branch resistance in a parallel circuit carries the largest branch current.

Accepted Answer

False

Question 5

Current divider predicts that the most current will flow in the parallel path of the most resistance.

Accepted Answer

False

Question 6

The total resistance of a parallel circuit is always greater than the largest resistor value.

Accepted Answer

False

Question 7

If one of the resistors opens in a parallel circuit branch, the total resistance of the circuit will decrease.

Accepted Answer

False

Question 8

The total resistance in a parallel circuit is always less than the least resistor.

Accepted Answer

True

Question 9

The total power dissipated is 4.8 watts.

Accepted Answer

False

Question 10

If a branch opens in a parallel circuit, the total circuit resistance decreases.

Accepted Answer

False

Question 11

The total resistance in a parallel circuit is always greater than the lowest-value branch resistor.

Accepted Answer

False

Question 12

The voltage in a parallel circuit is the same across each branch of the circuit.

Accepted Answer

True

Question 13

The total current entering a junction may be different from the total current leaving the junction.

Accepted Answer

False

Question 14

If one branch shorts out in a parallel circuit, the other branches are not affected.

Accepted Answer

False

Question 15

Parallel circuits have only one path for current.

Accepted Answer

False

Question 16

The total power in a parallel circuit equals the sum of the individual branch powers.

Accepted Answer

True

Question 17

If two equal resistors are connected in parallel, they will carry identical currents.

Accepted Answer

True

Question 18

The total resistance of like value resistors in parallel is equal to the value of the resistors multiplied by the number of resistors used.

Accepted Answer

False

Question 19

The total resistance is 480 Ω.

Accepted Answer

True

Question 20

The voltages across all components in parallel are equal.

Accepted Answer

True

Parallel Circuits Questions