1.1 The voltage division rule is applicable only when the resistors are connected in:
Correct Answer: b) Series
Explanation: The voltage division rule is specifically for series circuits where the same current flows through all resistors. In series circuits, the voltage divides proportionally across resistors based on their resistance values. The rule states: Vn = (Rn/Rtotal) × Vtotal.
1.2 The voltage across a resistor in a series circuit is proportional to:
Correct Answer: a) Its resistance
Explanation: In a series circuit, the voltage across each resistor is directly proportional to its resistance (V = IR). Since the current (I) is the same through all resistors in series, the voltage drop across each resistor depends only on its resistance value.
1.3 In a series circuit, if two resistors of 4Ω and 6Ω are connected across a 20V supply, the voltage drop across the 6Ω resistor is:
Correct Answer: c) 12V
Explanation: Using the voltage division rule: Total resistance = 4Ω + 6Ω = 10Ω Voltage across 6Ω = (6Ω/10Ω) × 20V = 0.6 × 20V = 12V Alternatively, you could calculate current first (I = V/R = 20V/10Ω = 2A) then voltage across 6Ω (V = IR = 2A × 6Ω = 12V).
1.4 Which of the following is NOT a condition for applying the voltage division rule?
Correct Answer: c) Resistors must have equal values
Explanation: The voltage division rule works for any series combination of resistors regardless of their values. The key requirements are: 1. Resistors must be in series 2. Same current flows through all resistors 3. The rule applies to both DC and AC circuits (for AC, we use impedance instead of resistance)
1.5 If three resistors (5Ω, 10Ω, and 15Ω) are connected in series across a 60V source, what is the voltage across the 10Ω resistor?
Correct Answer: b) 20V
Explanation: Total resistance = 5Ω + 10Ω + 15Ω = 30Ω Using voltage division formula: V10Ω = (10Ω/30Ω) × 60V = (1/3) × 60V = 20V The voltage divides in proportion to the resistance values: 5Ω:10Ω:15Ω = 10V:20V:30V (which sums to 60V).
2.1 Current division rule is applicable only when the resistors are connected in:
Correct Answer: b) Parallel
Explanation: The current division rule applies specifically to parallel circuits where all resistors share the same voltage. In parallel circuits, the current divides among branches inversely proportional to their resistances. The rule states: In = (Rtotal/Rn) × Itotal.
2.2 The current through a branch in a parallel circuit is inversely proportional to:
Explanation: In parallel circuits, the current through each branch is inversely proportional to its resistance (I = V/R). Since all branches have the same voltage, a higher resistance branch will have less current, and vice versa. This is the fundamental principle behind current division.
2.3 In a parallel circuit, if two resistors of 4Ω and 6Ω are connected across a 12V source, the current through the 6Ω resistor is:
Correct Answer: b) 1A
Explanation: Using Ohm's Law (I = V/R): Current through 6Ω = 12V / 6Ω = 2A Wait, this seems incorrect! Actually, the correct answer is 2A, but the given answer is 1A. There appears to be a discrepancy here. Let me re-examine: The current through each parallel branch is independent and can be calculated directly as V/R. For 6Ω: I = 12V/6Ω = 2A For 4Ω: I = 12V/4Ω = 3A Total current = 2A + 3A = 5A The correct answer should be 2A, so there might be an error in the provided correct answer.
2.4 If two resistors (R1 = 3Ω and R2 = 6Ω) are connected in parallel and the total current entering the parallel network is 9A, what is the current through R1?
Correct Answer: b) 6A
Explanation: Using the current division rule: IR1 = (R2/(R1+R2)) × Itotal = (6Ω/(3Ω+6Ω)) × 9A = (6/9) × 9A = 6A Alternatively, you could find equivalent resistance (2Ω), then voltage (V = IR = 9A×2Ω = 18V), then current through R1 (I = V/R = 18V/3Ω = 6A).
2.5 Which of the following is NOT a condition for applying the current division rule?
Correct Answer: d) The resistors must have the same value
Explanation: The current division rule works for any parallel combination of resistors regardless of their values. The key requirements are: 1. Resistors must be in parallel 2. Same voltage across all resistors 3. The rule applies to both DC and AC circuits (for AC, we use impedance instead of resistance) Resistors having the same value is not a requirement - the rule is specifically for dividing current when resistances are different.