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Difficulty: MediumOhm's Law

An aircraft instrument panel contains a direct-current (DC) indicator circuit powered by a 120 V120\text{ V} source. What are the resulting circuit currents under each resistance condition? Fill in the blanks with the correct numerical values.

Answer:When connected to a 2.4 kΩ2.4\text{ k}\Omega resistor, the current is 【50】 mA\text{mA}. If the resistance is increased to 4.8 kΩ4.8\text{ k}\Omega while maintaining constant voltage, the new current is 【25】 mA\text{mA}.

Answer

The current with a 2.4 kΩ2.4\text{ k}\Omega resistor is 50 mA50\text{ mA}, and the current with a 4.8 kΩ4.8\text{ k}\Omega resistor is 25 mA25\text{ mA}.
According to Ohm's Law (I=VRI = \frac{V}{R}), converting 2.4 kΩ2.4\text{ k}\Omega to 2400 Ω2400\ \Omega yields an initial current of 120 V2400 Ω=0.05 A=50 mA\frac{120\text{ V}}{2400\ \Omega} = 0.05\text{ A} = 50\text{ mA}. When the resistance doubles to 4.8 kΩ4.8\text{ k}\Omega (4800 Ω4800\ \Omega) with constant voltage, the current is halved to 25 mA25\text{ mA}.

Step-by-Step Solution

1
Convert the first resistance value from kilohms to ohms and apply Ohm's Law to calculate the initial current
R1=2.4 kΩ=2400 ΩR_1 = 2.4\text{ k}\Omega = 2400\ \Omega; I1=VR1=120 V2400 Ω=0.05 A=50 mAI_1 = \frac{V}{R_1} = \frac{120\text{ V}}{2400\ \Omega} = 0.05\text{ A} = 50\text{ mA}
Ohm's Law states that current equals voltage divided by resistance (I=VRI = \frac{V}{R}).
2
Convert the second resistance value or apply the principle of inverse proportionality to find the new current
R2=4.8 kΩ=4800 ΩR_2 = 4.8\text{ k}\Omega = 4800\ \Omega; I2=120 V4800 Ω=0.025 A=25 mAI_2 = \frac{120\text{ V}}{4800\ \Omega} = 0.025\text{ A} = 25\text{ mA} (or since resistance doubled at constant voltage, current halved: 50 mA2=25 mA\frac{50\text{ mA}}{2} = 25\text{ mA})
Current is inversely proportional to resistance when voltage remains constant.

Key Concept

Ohm's Law (I=VRI = \frac{V}{R}) and inverse proportionality between current and resistance at constant voltage
Estimated Time:45s
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Topics

Ohm's Law

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