Equivalent Resistance for Series Resistors: Worked Example

📚 Quick Study Guide

• 💡Resistors in series are connected end-to-end along a single path.
• 🔢The total resistance (equivalent resistance) of resistors in series is the sum of their individual resistances.
• 📏The formula for equivalent resistance ($R_{eq}$) in a series circuit with 'n' resistors is: $R_{eq} = R_1 + R_2 + R_3 + ... + R_n$
• ⚡The current is the same through each resistor in a series circuit.
• 📊The voltage drops across each resistor add up to the total voltage across the series combination.

🧪 Practice Quiz

1. Question 1: Three resistors with values of 10 $\Omega$, 20 $\Omega$, and 30 $\Omega$ are connected in series. What is the equivalent resistance?
   1. 10 $\Omega$
   2. 20 $\Omega$
   3. 30 $\Omega$
   4. 60 $\Omega$
2. Question 2: If four resistors, each with a resistance of 5 $\Omega$, are connected in series, what is the total resistance?
   1. 5 $\Omega$
   2. 10 $\Omega$
   3. 15 $\Omega$
   4. 20 $\Omega$
3. Question 3: A series circuit contains a 15 $\Omega$ resistor and a 25 $\Omega$ resistor. What is the equivalent resistance of the circuit?
   1. 10 $\Omega$
   2. 15 $\Omega$
   3. 25 $\Omega$
   4. 40 $\Omega$
4. Question 4: What happens to the equivalent resistance when you add more resistors in series?
   1. It decreases.
   2. It stays the same.
   3. It increases.
   4. It becomes zero.
5. Question 5: Two resistors are in series. If the equivalent resistance is 50 $\Omega$ and one resistor is 20 $\Omega$, what is the value of the other resistor?
   1. 20 $\Omega$
   2. 30 $\Omega$
   3. 50 $\Omega$
   4. 70 $\Omega$
6. Question 6: A circuit has three resistors in series with values of 5 $\Omega$, 10 $\Omega$, and an unknown resistance R. If the equivalent resistance is 25 $\Omega$, what is the value of R?
   1. 5 $\Omega$
   2. 10 $\Omega$
   3. 15 $\Omega$
   4. 20 $\Omega$
7. Question 7: A 3 $\Omega$ and a 6 $\Omega$ resistor are connected in series to a 12V battery. What is the current flowing through the 3 $\Omega$ resistor?
   1. 4 A
   2. 2 A
   3. 1 A
   4. 0.5 A