PRELIMINARY STAGE 2026
Contest 16
Tamale SHS: 68 points
Kalpohin SHS: 41 points
Wenchi Methodist SHS: 30 points
Contest 17
Kadjebi Asato SHS: 56 points
Ahantaman Girls’ SHS: 48 points
Ada SHTS, Sege: 35 points
Contest 18
Anglican SHS, Kumasi: 69 points
Namong SHTS: 28 points
Shama SHS: 25 points
ROUND 2 - SPEED RACE
QUESTION
Find the equivalent inductance of two parallel inductors, each of inductance 8 $\mu$H.
ANSWER: 4 $\mu$H
SOLUTION:
$L_{\text{eq}} = \dfrac{L}{2}$
$L = 8\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{8}{2}$
$L_{\text{eq}} = 4\ \mu\text{H}$
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PRACTICE QUESTIONS
1. QUESTION: Find the equivalent inductance of a 12 μH inductor and a 24 μH inductor connected in parallel.
ANSWER: 8.0 μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 36\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{12 \times 24}{36}$
$L_{\text{eq}} = \dfrac{24}{3}$
$L_{\text{eq}} = 8.0\text{ μH}$
2. QUESTION: Find the equivalent inductance of a 6.0 μH inductor and a 12 μH inductor connected in parallel.
ANSWER: 4.0 μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 18.0\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{6.0 \times 12}{18.0}$
$L_{\text{eq}} = \dfrac{12}{3}$
$L_{\text{eq}} = 4.0\text{ μH}$
3. QUESTION: Find the equivalent inductance of a 18 μH inductor and a 36 μH inductor connected in parallel.
ANSWER: 12 μH or $1.2\times10^{1}$ μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 54\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{18 \times 36}{54}$
$L_{\text{eq}} = \dfrac{36}{3}$
$L_{\text{eq}} = 12\text{ μH}$
4. QUESTION: Find the equivalent inductance of a 24 μH inductor and a 72 μH inductor connected in parallel.
ANSWER: 18 μH or $1.8\times10^{1}$ μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 96\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{24 \times 72}{96}$
$L_{\text{eq}} = \dfrac{72}{4}$
$L_{\text{eq}} = 18\text{ μH}$
5. QUESTION: Find the equivalent inductance of a 12 μH inductor and a 36 μH inductor connected in parallel.
ANSWER: 9.0 μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 48\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{12 \times 36}{48}$
$L_{\text{eq}} = \dfrac{36}{4}$
$L_{\text{eq}} = 9.0\text{ μH}$
6. QUESTION: Find the equivalent inductance of a 21 μH inductor and a 28 μH inductor connected in parallel.
ANSWER: 12 μH or $1.2\times10^{1}$ μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 49\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{21 \times 28}{49}$
$L_{\text{eq}} = \dfrac{3 \times 28}{7}$
$L_{\text{eq}} = 3 \times 4$
$L_{\text{eq}} = 12\text{ μH}$
7. QUESTION: Find the equivalent inductance of a 16 μH inductor and a 48 μH inductor connected in parallel.
ANSWER: 12 μH or $1.2\times10^{1}$ μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 64\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{16 \times 48}{64}$
$L_{\text{eq}} = \dfrac{48}{4}$
$L_{\text{eq}} = 12\text{ μH}$
8. QUESTION: Find the equivalent inductance of a 28 μH inductor and a 84 μH inductor connected in parallel.
ANSWER: 21 μH or $2.1\times10^{1}$ μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 112\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{28 \times 84}{112}$
$L_{\text{eq}} = \dfrac{84}{4}$
$L_{\text{eq}} = 21\text{ μH}$
9. QUESTION: Find the equivalent inductance of a 9.0 μH inductor and a 18 μH inductor connected in parallel.
ANSWER: 6.0 μH
SOLUTION:
$L_{\text{eq}} = \dfrac{L_1L_2}{L_1 + L_2}$
$L_1 + L_2 = 27.0\ \mu\text{H}$
$L_{\text{eq}} = \dfrac{9.0 \times 18}{27.0}$
$L_{\text{eq}} = \dfrac{18}{3}$
$L_{\text{eq}} = 6.0\text{ μH}$