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Difficulty: HardOhm's Law Calculations and Concepts

A DC workbench circuit connected to a fixed-voltage power supply draws a current of 8 mA8\text{ mA} through a 1.5 kΩ1.5\text{ k}\Omega resistor. If the resistor is replaced with a 6.0 kΩ6.0\text{ k}\Omega resistor while the supply voltage remains unchanged, what is the new current flowing through the circuit?

  1. A
    32 mA32\text{ mA}
  2. 2 mA2\text{ mA}Answer
  3. C
    12 mA12\text{ mA}
  4. D
    2 A2\text{ A}

Answer

2 mA2\text{ mA}
The correct current is 2 mA2\text{ mA}. First, applying Ohm's Law to the initial state yields a constant supply voltage of V=I×R=(8 mA)×(1.5 kΩ)=12 VV = I \times R = (8\text{ mA}) \times (1.5\text{ k}\Omega) = 12\text{ V}. When the resistance increases to 6.0 kΩ6.0\text{ k}\Omega, the new current is calculated as I=VR=12 V6.0 kΩ=2 mAI = \frac{V}{R} = \frac{12\text{ V}}{6.0\text{ k}\Omega} = 2\text{ mA}. Proportional reasoning confirms this: quadrupling resistance at constant voltage reduces current to one-fourth of its initial value (8 mA÷4=2 mA8\text{ mA} \div 4 = 2\text{ mA}).

Step-by-Step Solution

1
Calculate the fixed supply voltage (VV) using the initial current and resistance values.
V=I1×R1=(8 mA)×(1.5 kΩ)=(0.008 A)×(1500 Ω)=12 VV = I_1 \times R_1 = (8\text{ mA}) \times (1.5\text{ k}\Omega) = (0.008\text{ A}) \times (1500\ \Omega) = 12\text{ V}
Ohm's Law states that voltage is the product of current and resistance.
2
Calculate the new current (I2I_2) using the constant supply voltage and the new resistance value.
I2=VR2=12 V6.0 kΩ=12 V6000 Ω=0.002 A=2 mAI_2 = \frac{V}{R_2} = \frac{12\text{ V}}{6.0\text{ k}\Omega} = \frac{12\text{ V}}{6000\ \Omega} = 0.002\text{ A} = 2\text{ mA}
Current equals voltage divided by resistance. Alternatively, since resistance increased by a factor of 4 (1.5 kΩ1.5\text{ k}\Omega to 6.0 kΩ6.0\text{ k}\Omega) at constant voltage, current must decrease by a factor of 4 (8 mA/4=2 mA8\text{ mA} / 4 = 2\text{ mA}).

Key Concept

Ohm's Law and inverse proportionality between current and resistance at constant voltage
Estimated Time:1m 0s
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Topics

Ohm's Law Calculations and Concepts

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