Examkin

Question

Difficulty: MediumOhm's Law

A radar transceiver module operates on a 45 V45\text{ V} direct-current (DC) power line. When the module is active, a series ammeter registers a current of 15 mA15\text{ mA}. What is the total electrical resistance of the module?

  1. A
    3 Ω3\ \Omega
  2. 3 kΩ3\text{ k}\OmegaAnswer
  3. C
    675 Ω675\ \Omega
  4. D
    333 Ω333\ \Omega

Answer

3 kΩ3\text{ k}\Omega (or 3,000 Ω3,000\ \Omega)
According to Ohm's Law, resistance is the quotient of voltage divided by current (R=VIR = \frac{V}{I}). Converting 15 mA15\text{ mA} to standard units gives 0.015 A0.015\text{ A}. Dividing the 45 V45\text{ V} potential difference by 0.015 A0.015\text{ A} results in 3,000 Ω3,000\ \Omega, which is equivalent to 3 kΩ3\text{ k}\Omega.

Step-by-Step Solution

1
Convert the current measurement from milliamperes to base amperes.
I=15 mA=15×10−3 A=0.015 AI = 15\text{ mA} = 15 \times 10^{-3}\text{ A} = 0.015\text{ A}
Ohm's Law calculations require current to be expressed in standard SI units (amperes) to yield resistance in ohms.
2
Rearrange Ohm's Law (V=I×RV = I \times R) to solve for resistance (RR).
R=VIR = \frac{V}{I}
Isolating the unknown variable allows direct substitution of known circuit values.
3
Substitute the voltage and current values into the rearranged formula.
R=45 V0.015 A=3,000 Ω=3 kΩR = \frac{45\text{ V}}{0.015\text{ A}} = 3,000\ \Omega = 3\text{ k}\Omega
Dividing the potential difference by the current yields the total circuit resistance.

Key Concept

Ohm's Law defines the fundamental linear relationship between voltage, current, and resistance (V=I×RV = I \times R).
Estimated Time:45s
Rate this question

Topics

Ohm's Law

More questions from this topic