PRELIMINARY STAGE 2026
Contest 40
Konongo Odumase SHS: 45 points
Our Lady of Mt. Carmel Girls' SHS: 31 points
Juaben SHS: 28 points
Contest 41
St. Monica's SHS: 40 points
Amenfiman SHS: 37 points
Tema Methodist Day SHS: 15 points
Contest 42
Accra High School: 33 points
Ghana SHS, Tamale: 32 points
Sunyani SHS: 31 points
ROUND 2 - SPEED RACE
QUESTION
A resistor network is made up of a 5 $\Omega$ resistor in series with a parallel combination of two 10 $\Omega$ resistors.
Find the voltage across the 5 $\Omega$ resistor when the voltage across the whole network is 8 V.
ANSWER: 4 V
SOLUTION:
Find the parallel combination of the two 10 $\Omega$ resistors:
$R_{\text{parallel}} = \dfrac{10}{2}$
$R_{\text{parallel}} = 5\ \Omega$
Since the series resistor ($5\ \Omega$) and the parallel block ($5\ \Omega$) are identical, the total voltage splits exactly in half:
$V_{5\Omega} = \dfrac{8}{2}$
$V_{5\Omega} = 4\text{ V}$
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PRACTICE QUESTIONS
1. QUESTION: A resistor network is made up of a 4.0 Ω resistor in series with a parallel combination of two 12 Ω resistors. Find the voltage across the 4.0 Ω resistor when the voltage across the whole network is 9.0 V.
ANSWER: 3.6 V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{12}{2}$
$R_{\text{parallel}} = 6\ \Omega$
$R_{\text{total}} = 4.0 + 6$
$R_{\text{total}} = 10.0\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{9.0 \times 4.0}{10.0}$
$V_1 = \dfrac{9 \times 2}{5}$
$V_1 = 3.6\text{ V}$
2. QUESTION: A resistor network is made up of a 3.0 Ω resistor in series with a parallel combination of two 18 Ω resistors. Find the voltage across the 3.0 Ω resistor when the voltage across the whole network is 24 V.
ANSWER: 6.0 V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{18}{2}$
$R_{\text{parallel}} = 9\ \Omega$
$R_{\text{total}} = 3.0 + 9$
$R_{\text{total}} = 12.0\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{24 \times 3.0}{12.0}$
$V_1 = 2 \times 3$
$V_1 = 6.0\text{ V}$
3. QUESTION: A resistor network is made up of a 8.0 Ω resistor in series with a parallel combination of two 16 Ω resistors. Find the voltage across the 8.0 Ω resistor when the voltage across the whole network is 15 V.
ANSWER: 7.5 V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{16}{2}$
$R_{\text{parallel}} = 8\ \Omega$
$R_{\text{total}} = 8.0 + 8$
$R_{\text{total}} = 16.0\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{15 \times 8.0}{16.0}$
$V_1 = \dfrac{15}{2}$
$V_1 = 7.5\text{ V}$
4. QUESTION: A resistor network is made up of a 2.0 Ω resistor in series with a parallel combination of two 12 Ω resistors. Find the voltage across the 2.0 Ω resistor when the voltage across the whole network is 16 V.
ANSWER: 4.0 V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{12}{2}$
$R_{\text{parallel}} = 6\ \Omega$
$R_{\text{total}} = 2.0 + 6$
$R_{\text{total}} = 8.0\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{16 \times 2.0}{8.0}$
$V_1 = 2 \times 2$
$V_1 = 4.0\text{ V}$
5. QUESTION: A resistor network is made up of a 6.0 Ω resistor in series with a parallel combination of two 24 Ω resistors. Find the voltage across the 6.0 Ω resistor when the voltage across the whole network is 9.0 V.
ANSWER: 3.0 V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{24}{2}$
$R_{\text{parallel}} = 12\ \Omega$
$R_{\text{total}} = 6.0 + 12$
$R_{\text{total}} = 18.0\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{9.0 \times 6.0}{18.0}$
$V_1 = \dfrac{6}{2}$
$V_1 = 3.0\text{ V}$
6. QUESTION: A resistor network is made up of a 9.0 Ω resistor in series with a parallel combination of two 6.0 Ω resistors. Find the voltage across the 9.0 Ω resistor when the voltage across the whole network is 12 V.
ANSWER: 9.0 V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{6.0}{2}$
$R_{\text{parallel}} = 3\ \Omega$
$R_{\text{total}} = 9.0 + 3$
$R_{\text{total}} = 12.0\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{12 \times 9.0}{12.0}$
$V_1 = 9.0\text{ V}$
7. QUESTION: A resistor network is made up of a 1.5 Ω resistor in series with a parallel combination of two 9.0 Ω resistors. Find the voltage across the 1.5 Ω resistor when the voltage across the whole network is 6.0 V.
ANSWER: 1.5 V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{9.0}{2}$
$R_{\text{parallel}} = 4.5\ \Omega$
$R_{\text{total}} = 1.5 + 4.5$
$R_{\text{total}} = 6.0\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{6.0 \times 1.5}{6.0}$
$V_1 = \dfrac{6 \times 15\times10^{-1}}{6}$
$V_1 = 1.5\text{ V}$
8. QUESTION: A resistor network is made up of a 12 Ω resistor in series with a parallel combination of two 24 Ω resistors. Find the voltage across the 12 Ω resistor when the voltage across the whole network is 16 V.
ANSWER: 8.0 V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{24}{2}$
$R_{\text{parallel}} = 12\ \Omega$
$R_{\text{total}} = 12 + 12$
$R_{\text{total}} = 24\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{16 \times 12}{24}$
$V_1 = \dfrac{16}{2}$
$V_1 = 8.0\text{ V}$
9. QUESTION: A resistor network is made up of a 4.5 Ω resistor in series with a parallel combination of two 3.0 Ω resistors. Find the voltage across the 4.5 Ω resistor when the voltage across the whole network is 16 V.
ANSWER: 12 V or $1.2\times10^{1}$ V
SOLUTION:
$R_{\text{parallel}} = \dfrac{R_2}{2}$ (two equal resistors)
$R_{\text{parallel}} = \dfrac{3.0}{2}$
$R_{\text{parallel}} = 1.5\ \Omega$
$R_{\text{total}} = 4.5 + 1.5$
$R_{\text{total}} = 6.0\ \Omega$
$V_1 = V \times \dfrac{R_1}{R_{\text{total}}}$
$V_1 = \dfrac{16 \times 4.5}{6.0}$
$V_1 = \dfrac{16 \times 45\times10^{-1}}{6}$
$V_1 = \dfrac{16 \times 15}{2} \times10^{-1}$
$V_1 = 8 \times 15 \times10^{-1}$
$V_1 = 12\text{ V}$