Circuits Fundamentals Quiz: Test Your Circuit Analysis Skills Quiz

Challenge your understanding of circuits with these essential questions covering Ohm's Law, series and parallel networks, Kirchoff's rules, and key analysis techniques. Perfect for students and enthusiasts aiming to sharpen their circuit analysis knowledge and problem-solving abilities.

1. Identifying Ohm's Law

   Which equation correctly represents Ohm's Law for a simple resistor circuit with a voltage source?

   1. V = I + R
   2. I = V × R
   3. V = I × R
   4. P = V × R

   Explanation: Ohm's Law states that the voltage (V) across a resistor is the product of the current (I) through it and its resistance (R), or V = I × R. The option P = V × R does not correctly relate voltage and resistance and actually gives incorrect units. Option I = V × R is not correct, as current should be calculated by dividing voltage by resistance. The option V = I + R incorrectly adds the terms instead of multiplying, which is not how Ohm’s Law operates.

2. Series vs. Parallel Resistance

   Given three resistors (5 Ω, 10 Ω, and 15 Ω) connected in series, what is the total resistance of this circuit?

   1. 5 Ω
   2. 30 Ω
   3. 1.67 Ω
   4. 10 Ω

   Explanation: For resistors in series, you sum the resistance values directly, so 5 Ω + 10 Ω + 15 Ω = 30 Ω. Option 1.67 Ω is incorrect and would be the reciprocal sum used for parallel resistors. The options 10 Ω and 5 Ω represent individual resistors, not the total series resistance. Therefore, 30 Ω is the correct total resistance for a series connection.

3. Kirchhoff’s Current Law Application

   If 6 A of current enters a node and splits into two branches, with one branch carrying 4 A, what is the current in the other branch according to Kirchhoff’s Current Law?

   1. 4 A
   2. 10 A
   3. 2 A
   4. 0.67 A

   Explanation: Kirchhoff’s Current Law states that the total current entering a node must equal the total current leaving the node. Therefore, if 6 A enters and one branch carries 4 A away, the other must carry 2 A to account for all incoming current. The options 10 A and 0.67 A do not match the total current required by the law. The option 4 A mistakenly repeats the current in one branch rather than solving for the other.

4. Voltage Division in Series Circuits

   In a series circuit with a 20 V power supply and two resistors (5 Ω and 15 Ω), what is the voltage drop across the 15 Ω resistor?

   1. 15 V
   2. 10 V
   3. 20 V
   4. 5 V

   Explanation: The voltage drop across a resistor in series is given by V = (R_individual / R_total) × supplied voltage. The total resistance is 20 Ω, so the 15 Ω resistor's share is (15/20) × 20 V = 15 V. Options 5 V and 10 V misapply the division ratio or select the wrong resistor. 20 V would be the full supply voltage, which is not the drop across just one resistor.

5. Capacitors in Parallel

   What is the equivalent capacitance when three capacitors of 2 μF, 3 μF, and 5 μF are connected in parallel?

   1. 2 μF
   2. 0.5 μF
   3. 3.33 μF
   4. 10 μF

   Explanation: Capacitors in parallel simply add, so 2 μF + 3 μF + 5 μF = 10 μF for the total capacitance. The option 0.5 μF is incorrect and could result from an incorrect use of the formula for series capacitors. 3.33 μF would be relevant if the capacitors were in series, not parallel. 2 μF is just one capacitor's value, not the total capacitance across the parallel network.