High-voltage DC application: determine the current when 18 kV is applied across a 15 kΩ resistance (state the result in appropriate SI units).
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A1.2 A
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B12 A
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C120 mA
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D12 mA
Answer
Correct Answer: 1.2 A
Explanation
Introduction / Context:Ohm’s law scales easily to kilovolt and kilo-ohm ranges common in high-voltage testing and insulation checks. Accurate unit handling (kV, kΩ) prevents order-of-magnitude mistakes and ensures safe design margins.
Given Data / Assumptions:
- Voltage V = 18 kV = 18,000 V.
- Resistance R = 15 kΩ = 15,000 Ω.
- Use I = V / R for a purely resistive element.
Concept / Approach:
Convert both quantities to base SI units (volts, ohms), then compute current. Alternatively, use ratio of prefixes directly: kV/kΩ cancels the kilo factor, leaving amperes.
Step-by-Step Solution:
Convert: V = 18,000 V, R = 15,000 Ω.Compute I = V / R = 18,000 / 15,000 = 1.2 A.No further scaling is needed; amperes is the correct SI unit for current.Verification / Alternative check:
Prefix method: 18 kV / 15 kΩ = (18/15) kV/kΩ = 1.2 A because k cancels. Consistent with the calculation above.
Why Other Options Are Wrong:
12 A is 10× too large; 120 mA is 10× too small; 12 mA is 100× too small.
Common Pitfalls:
Failing to convert kV and kΩ consistently; treating kilo as 1024 instead of 1000 in SI electrical units.
Final Answer:
1.2 A