QUARTER FINAL STAGE 2024
Yilo Krobo
Koforidua Senior High Tech
KNUST SHS
ROUND 2 - SPEED RACE
QUESTION
Find the power dissipation of a circuit composed of a 20 ohm resistor in series with a 30 ohm resistor when the circuit draws 4 amperes.
ANSWER: 800 W
SOLUTION:
Resistors in series add directly:
$R_{total}=20+30$
$R_{total}=50\ \Omega$
Use $P=I^2R$ with the total resistance:
$P=4^2\times50$
$P=16\times50$
$P=800\text{ W}$
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PRACTICE QUESTIONS
1. QUESTION: Find the power dissipation of a circuit made of a 5.0 Ω resistor in series with a 7.0 Ω resistor when the circuit draws 2.0 A.
ANSWER: 48 W or $4.8\times10^{1}$ W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 5.0 + 7.0$
$R_{\text{total}} = 12.0\ \Omega$
$P = I^2R_{\text{total}}$
$P = 2.0 \times 2.0 \times 12.0$
$P = 48\text{ W}$
2. QUESTION: Find the power dissipation of a circuit made of a 12 Ω resistor in series with a 12 Ω resistor when the circuit draws 0.50 A.
ANSWER: 6.0 W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 12 + 12$
$R_{\text{total}} = 24\ \Omega$
$P = I^2R_{\text{total}}$
$P = 0.50 \times 0.50 \times 24$
$P = 5\times10^{-1} \times 5\times10^{-1} \times 24$
$P = 5 \times 5 \times 24 \times10^{-2}$
$P = 6.0\text{ W}$
3. QUESTION: Find the power dissipation of a circuit made of a 1.5 Ω resistor in series with a 3.5 Ω resistor when the circuit draws 3.0 A.
ANSWER: 45 W or $4.5\times10^{1}$ W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 1.5 + 3.5$
$R_{\text{total}} = 5.0\ \Omega$
$P = I^2R_{\text{total}}$
$P = 3.0 \times 3.0 \times 5.0$
$P = 45\text{ W}$
4. QUESTION: Find the power dissipation of a circuit made of a 1.5 Ω resistor in series with a 2.5 Ω resistor when the circuit draws 2.5 A.
ANSWER: 25 W or $2.5\times10^{1}$ W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 1.5 + 2.5$
$R_{\text{total}} = 4.0\ \Omega$
$P = I^2R_{\text{total}}$
$P = 2.5 \times 2.5 \times 4.0$
$P = 25\times10^{-1} \times 25\times10^{-1} \times 4$
$P = 25 \times 25 \times 4 \times10^{-2}$
$P = 25$
$P = 25\text{ W}$
5. QUESTION: Find the power dissipation of a circuit made of a 11 Ω resistor in series with a 14 Ω resistor when the circuit draws 0.40 A.
ANSWER: 4.0 W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 11 + 14$
$R_{\text{total}} = 25\ \Omega$
$P = I^2R_{\text{total}}$
$P = 0.40 \times 0.40 \times 25$
$P = 4\times10^{-1} \times 4\times10^{-1} \times 25$
$P = 4 \times 4 \times 25 \times10^{-2}$
$P = 4.0\text{ W}$
6. QUESTION: Find the power dissipation of a circuit made of a 1.2 Ω resistor in series with a 2.3 Ω resistor when the circuit draws 4.0 A.
ANSWER: 56 W or $5.6\times10^{1}$ W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 1.2 + 2.3$
$R_{\text{total}} = 3.5\ \Omega$
$P = I^2R_{\text{total}}$
$P = 4.0 \times 4.0 \times 3.5$
$P = 4 \times 4 \times 35\times10^{-1}$
$P = 56\text{ W}$
7. QUESTION: Find the power dissipation of a circuit made of a 2.5 Ω resistor in series with a 1.5 Ω resistor when the circuit draws 1.5 A.
ANSWER: 9.0 W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 2.5 + 1.5$
$R_{\text{total}} = 4.0\ \Omega$
$P = I^2R_{\text{total}}$
$P = 1.5 \times 1.5 \times 4.0$
$P = 15\times10^{-1} \times 15\times10^{-1} \times 4$
$P = 15 \times 15 \times 4 \times10^{-2}$
$P = 9.0\text{ W}$
8. QUESTION: Find the power dissipation of a circuit made of a 12 Ω resistor in series with a 13 Ω resistor when the circuit draws 0.80 A.
ANSWER: 16 W or $1.6\times10^{1}$ W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 12 + 13$
$R_{\text{total}} = 25\ \Omega$
$P = I^2R_{\text{total}}$
$P = 0.80 \times 0.80 \times 25$
$P = 8\times10^{-1} \times 8\times10^{-1} \times 25$
$P = 8 \times 8 \times 25 \times10^{-2}$
$P = 2 \times 8$
$P = 16\text{ W}$
9. QUESTION: Find the power dissipation of a circuit made of a 11 Ω resistor in series with a 14 Ω resistor when the circuit draws 1.2 A.
ANSWER: 36 W or $3.6\times10^{1}$ W
SOLUTION:
Resistors in series add directly:
$R_{\text{total}} = 11 + 14$
$R_{\text{total}} = 25\ \Omega$
$P = I^2R_{\text{total}}$
$P = 1.2 \times 1.2 \times 25$
$P = 12\times10^{-1} \times 12\times10^{-1} \times 25$
$P = 12 \times 12 \times 25 \times10^{-2}$
$P = 3 \times 12$
$P = 36\text{ W}$