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Difficulty: EasyOhm's Law

A 36 V36\text{ V} DC control circuit supplies power to a single heating element. An inline ammeter measures a steady current flow of 3 A3\text{ A} through the circuit. What is the electrical resistance of the heating element in ohms?

Answer: 12 Ω

Answer

12 ohms
According to Ohm's Law, resistance equals voltage divided by current (R=VIR = \frac{V}{I}). Dividing the source voltage of 36 V36\text{ V} by the current of 3 A3\text{ A} yields 12 Ω12\ \Omega.

Step-by-Step Solution

1
Identify the known electrical values provided in the problem
Voltage (VV) = 36 V36\text{ V}, Current (II) = 3 A3\text{ A}
Ohm's Law relates potential difference, current flow, and circuit resistance.
2
Rearrange Ohm's Law to express resistance in terms of voltage and current
R=VIR = \frac{V}{I}
Resistance is defined as the ratio of voltage across a component to the current flowing through it.
3
Substitute the numerical values into the equation and solve
R=36 V3 A=12 ΩR = \frac{36\text{ V}}{3\text{ A}} = 12\ \Omega
Dividing 36 by 3 gives the resistance directly in ohms.

Key Concept

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance (V=I×RV = I \times R, which rearranges to R=VIR = \frac{V}{I}).
Estimated Time:30s
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Topics

Ohm's Law

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