QUARTER FINAL STAGE 2026
Tamale SHS (Tamasco): 36 points
St. Hubert Minor Seminary SHS: 33 points
Labone SHS: 14 points
QUESTION
Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at $5.0$ kA/s if the mutual inductance of the circuit is $2.4$ mH.
ANSWER: $12$ V
SOLUTION:
$M = 2.4\text{ mH}$
$M = 2.4 \times 10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 5.0\text{ kA/s}$
$\dfrac{dI}{dt} = 5.0 \times 10^3\text{ A/s}$
$\varepsilon = M\dfrac{dI}{dt}$
$\varepsilon = (2.4 \times 10^{-3}\text{ H})(5.0 \times 10^3\text{ A/s})$
$\varepsilon = (2.4 \times 5.0) \times (10^{-3} \times 10^3)\text{ V}$
$\varepsilon = 12.0 \times 10^0\text{ V}$
$\varepsilon = 12\text{ V}$
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PRACTICE QUESTIONS
1. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 4.0 kA/s if the mutual inductance of the circuit is 1.5 mH.
ANSWER: 6.0 V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 1.5\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 4.0\times10^{3}\text{ A/s}$
$\varepsilon = 1.5\times10^{-3} \times 4.0\times10^{3}$
$\varepsilon = 15\times10^{-4} \times 4\times10^{3}$
$\varepsilon = 15 \times 4 \times10^{-1}$
$\varepsilon = 6.0\text{ V}$
2. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 2.5 kA/s if the mutual inductance of the circuit is 3.2 mH.
ANSWER: 8.0 V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 3.2\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 2.5\times10^{3}\text{ A/s}$
$\varepsilon = 3.2\times10^{-3} \times 2.5\times10^{3}$
$\varepsilon = 32\times10^{-4} \times 25\times10^{2}$
$\varepsilon = 32 \times 25 \times10^{-2}$
$\varepsilon = 8.0\text{ V}$
3. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 7.5 kA/s if the mutual inductance of the circuit is 0.80 mH.
ANSWER: 6.0 V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 0.80\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 7.5\times10^{3}\text{ A/s}$
$\varepsilon = 0.80\times10^{-3} \times 7.5\times10^{3}$
$\varepsilon = 8\times10^{-4} \times 75\times10^{2}$
$\varepsilon = 8 \times 75 \times10^{-2}$
$\varepsilon = 6.0\text{ V}$
4. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 2.0 kA/s if the mutual inductance of the circuit is 4.5 mH.
ANSWER: 9.0 V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 4.5\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 2.0\times10^{3}\text{ A/s}$
$\varepsilon = 4.5\times10^{-3} \times 2.0\times10^{3}$
$\varepsilon = 45\times10^{-4} \times 2\times10^{3}$
$\varepsilon = 45 \times 2 \times10^{-1}$
$\varepsilon = 9.0\text{ V}$
5. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 5.0 kA/s if the mutual inductance of the circuit is 1.2 mH.
ANSWER: 6.0 V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 1.2\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 5.0\times10^{3}\text{ A/s}$
$\varepsilon = 1.2\times10^{-3} \times 5.0\times10^{3}$
$\varepsilon = 12\times10^{-4} \times 5\times10^{3}$
$\varepsilon = 12 \times 5 \times10^{-1}$
$\varepsilon = 6.0\text{ V}$
6. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 6.0 kA/s if the mutual inductance of the circuit is 2.5 mH.
ANSWER: 15 V or $1.5\times10^{1}$ V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 2.5\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 6.0\times10^{3}\text{ A/s}$
$\varepsilon = 2.5\times10^{-3} \times 6.0\times10^{3}$
$\varepsilon = 25\times10^{-4} \times 6\times10^{3}$
$\varepsilon = 25 \times 6 \times10^{-1}$
$\varepsilon = 15\text{ V}$
7. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 1.5 kA/s if the mutual inductance of the circuit is 6.0 mH.
ANSWER: 9.0 V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 6.0\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 1.5\times10^{3}\text{ A/s}$
$\varepsilon = 6.0\times10^{-3} \times 1.5\times10^{3}$
$\varepsilon = 6\times10^{-3} \times 15\times10^{2}$
$\varepsilon = 6 \times 15 \times10^{-1}$
$\varepsilon = 9.0\text{ V}$
8. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 8.0 kA/s if the mutual inductance of the circuit is 0.60 mH.
ANSWER: 4.8 V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 0.60\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 8.0\times10^{3}\text{ A/s}$
$\varepsilon = 0.60\times10^{-3} \times 8.0\times10^{3}$
$\varepsilon = 6\times10^{-4} \times 8\times10^{3}$
$\varepsilon = 6 \times 8 \times10^{-1}$
$\varepsilon = 4.8\text{ V}$
9. QUESTION: Calculate the EMF induced in a circuit when the current in a nearby circuit is changing at 4.0 kA/s if the mutual inductance of the circuit is 3.5 mH.
ANSWER: 14 V or $1.4\times10^{1}$ V
SOLUTION:
$\varepsilon = M\dfrac{dI}{dt}$
$M = 3.5\times10^{-3}\text{ H}$
$\dfrac{dI}{dt} = 4.0\times10^{3}\text{ A/s}$
$\varepsilon = 3.5\times10^{-3} \times 4.0\times10^{3}$
$\varepsilon = 35\times10^{-4} \times 4\times10^{3}$
$\varepsilon = 35 \times 4 \times10^{-1}$
$\varepsilon = 14\text{ V}$