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To form a composite 16 μF, 1000V capacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors.
Correct answer is '32'. Can you explain this answer?
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To form a composite 16 μF, 1000Vcapacitor from a supply of identica...
To form a composite 16 µF, 1000V capacitor using 8 µF, 250V capacitors, we must consider both capacitance and voltage ratings.
Capacitance Calculation
- The required capacitance is 16 µF.
- Each capacitor has a capacitance of 8 µF.
- To achieve a total capacitance of 16 µF, we can connect two 8 µF capacitors in parallel:
- Total Capacitance in Parallel = C1 + C2 = 8 µF + 8 µF = 16 µF.
Thus, we need 2 capacitors in parallel to achieve the desired capacitance.
Voltage Rating Calculation
- Each capacitor is rated for 250V.
- The desired capacitor must withstand 1000V.
- To handle higher voltages, we can connect the capacitors in series. In series, voltage ratings add up:
- Total Voltage in Series = V1 + V2 + V3 + ... = n * 250V.
To achieve a voltage rating of 1000V:
- n * 250V >= 1000V,
- n >= 4.
Thus, we need 4 capacitors in series to meet the voltage requirement.
Combining Capacitance and Voltage Requirements
- To construct a composite capacitor that meets both the capacitance and voltage requirements:
- Use 4 capacitors in series to achieve 1000V.
- Each series group (4 capacitors) provides a total capacitance of 2 µF (since in series, C = 1/(1/C1 + 1/C2 + ...)).
To achieve a total of 16 µF:
- We need to connect 8 groups of 4 capacitors in series in parallel:
- Total Capacitors = 8 groups * 4 capacitors/group = 32 capacitors.
Thus, the minimum number of 8 µF, 250V capacitors needed to form a 16 µF, 1000V capacitor is 32.
Capacitance Calculation
- The required capacitance is 16 µF.
- Each capacitor has a capacitance of 8 µF.
- To achieve a total capacitance of 16 µF, we can connect two 8 µF capacitors in parallel:
- Total Capacitance in Parallel = C1 + C2 = 8 µF + 8 µF = 16 µF.
Thus, we need 2 capacitors in parallel to achieve the desired capacitance.
Voltage Rating Calculation
- Each capacitor is rated for 250V.
- The desired capacitor must withstand 1000V.
- To handle higher voltages, we can connect the capacitors in series. In series, voltage ratings add up:
- Total Voltage in Series = V1 + V2 + V3 + ... = n * 250V.
To achieve a voltage rating of 1000V:
- n * 250V >= 1000V,
- n >= 4.
Thus, we need 4 capacitors in series to meet the voltage requirement.
Combining Capacitance and Voltage Requirements
- To construct a composite capacitor that meets both the capacitance and voltage requirements:
- Use 4 capacitors in series to achieve 1000V.
- Each series group (4 capacitors) provides a total capacitance of 2 µF (since in series, C = 1/(1/C1 + 1/C2 + ...)).
To achieve a total of 16 µF:
- We need to connect 8 groups of 4 capacitors in series in parallel:
- Total Capacitors = 8 groups * 4 capacitors/group = 32 capacitors.
Thus, the minimum number of 8 µF, 250V capacitors needed to form a 16 µF, 1000V capacitor is 32.
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To form a composite 16 μF, 1000Vcapacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors.Correct answer is '32'. Can you explain this answer?
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To form a composite 16 μF, 1000Vcapacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors.Correct answer is '32'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about To form a composite 16 μF, 1000Vcapacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors.Correct answer is '32'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for To form a composite 16 μF, 1000Vcapacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors.Correct answer is '32'. Can you explain this answer?.
To form a composite 16 μF, 1000Vcapacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors.Correct answer is '32'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about To form a composite 16 μF, 1000Vcapacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors.Correct answer is '32'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for To form a composite 16 μF, 1000Vcapacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors.Correct answer is '32'. Can you explain this answer?.
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