SEMI FINAL STAGE 2025
Opoku Ware School (OWASS): 48 points
Achimota School: 27 points
St. Peter's SHS: 10 points
QUESTION
The dielectric strength of a certain polymer is $7.0\times10^7$ V/m and its dielectric constant is 2.2.
Find the minimum thickness of a 50.0 μF capacitor with the polymer completely filling the space between its plates that can withstand a potential difference of 28 V.
ANSWER: 0.40 μm.
SOLUTION:
$E_{\text{max}} = \dfrac{V}{d_{\text{min}}}$
$d_{\text{min}} = \dfrac{V}{E_{\text{max}}}$
$V = 28\text{ V}$
$E_{\text{max}} = 7.0\times10^7\text{ V/m}$
$d_{\text{min}} = \dfrac{28}{7.0\times10^7}$
$d_{\text{min}} = \dfrac{28}{7\times10^{7}}$
$d_{\text{min}} = 4.0\times10^{-7}\text{ m}$
$d_{\text{min}} = \dfrac{4.0}{10^7}$
$d_{\text{min}} = 0.40\times10^{-6}\text{ m}$
$d_{\text{min}} = 0.40\ \mu\text{m}$
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PRACTICE QUESTIONS
1. QUESTION: The dielectric strength of a polymer is $6.0\times10^{7}$ V/m and its dielectric constant is 2.5. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 24 V.
ANSWER: 0.40 μm or $4.0\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{24}{6.0\times10^{7}}$
$d = \dfrac{24}{6\times10^{7}}$
$d = 4.0\times10^{-7}\text{ m}$
$d = 0.40\ \mu\text{m}$
2. QUESTION: The dielectric strength of a polymer is $9.0\times10^{7}$ V/m and its dielectric constant is 3.0. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 36 V.
ANSWER: 0.40 μm or $4.0\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{36}{9.0\times10^{7}}$
$d = \dfrac{36}{9\times10^{7}}$
$d = 4.0\times10^{-7}\text{ m}$
$d = 0.40\ \mu\text{m}$
3. QUESTION: The dielectric strength of a polymer is $5.0\times10^{7}$ V/m and its dielectric constant is 2.2. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 15 V.
ANSWER: 0.30 μm or $3.0\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{15}{5.0\times10^{7}}$
$d = \dfrac{15}{5\times10^{7}}$
$d = 3.0\times10^{-7}\text{ m}$
$d = 0.30\ \mu\text{m}$
4. QUESTION: The dielectric strength of a polymer is $9.0\times10^{7}$ V/m and its dielectric constant is 4.0. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 45 V.
ANSWER: 0.50 μm or $5.0\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{45}{9.0\times10^{7}}$
$d = \dfrac{45}{9\times10^{7}}$
$d = 5.0\times10^{-7}\text{ m}$
$d = 0.50\ \mu\text{m}$
5. QUESTION: The dielectric strength of a polymer is $6.0\times10^{7}$ V/m and its dielectric constant is 3.5. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 18 V.
ANSWER: 0.30 μm or $3.0\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{18}{6.0\times10^{7}}$
$d = \dfrac{18}{6\times10^{7}}$
$d = 3.0\times10^{-7}\text{ m}$
$d = 0.30\ \mu\text{m}$
6. QUESTION: The dielectric strength of a polymer is $4.0\times10^{7}$ V/m and its dielectric constant is 2.4. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 28 V.
ANSWER: 0.70 μm or $7.0\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{28}{4.0\times10^{7}}$
$d = \dfrac{28}{4\times10^{7}}$
$d = 7.0\times10^{-7}\text{ m}$
$d = 0.70\ \mu\text{m}$
7. QUESTION: The dielectric strength of a polymer is $7.0\times10^{7}$ V/m and its dielectric constant is 2.8. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 35 V.
ANSWER: 0.50 μm or $5.0\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{35}{7.0\times10^{7}}$
$d = \dfrac{35}{7\times10^{7}}$
$d = 5.0\times10^{-7}\text{ m}$
$d = 0.50\ \mu\text{m}$
8. QUESTION: The dielectric strength of a polymer is $8.0\times10^{7}$ V/m and its dielectric constant is 3.2. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 12 V.
ANSWER: 0.15 μm or $1.5\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{12}{8.0\times10^{7}}$
$d = \dfrac{12}{8\times10^{7}}$
$d = \dfrac{3}{2} \times10^{-7}$
$d = 1.5\times10^{-7}\text{ m}$
$d = 0.15\ \mu\text{m}$
9. QUESTION: The dielectric strength of a polymer is $6.0\times10^{7}$ V/m and its dielectric constant is 2.0. Find the minimum thickness of polymer in a capacitor that can withstand a potential difference of 54 V.
ANSWER: 0.90 μm or $9.0\times10^{-1}$ μm
SOLUTION:
$E_{\max} = \dfrac{V}{d_{\min}}$
$d_{\min} = \dfrac{V}{E_{\max}}$
$d = \dfrac{54}{6.0\times10^{7}}$
$d = \dfrac{54}{6\times10^{7}}$
$d = 9.0\times10^{-7}\text{ m}$
$d = 0.90\ \mu\text{m}$