Question 21 of 31beginner🔧 ApplyNumerical3 marks

When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.

Correct Answer

The value of the resistance is 4800 Ω (or 4.8 kΩ).

Exercise: EXERCISES | Q: 8 | (Page Page 23)
For More Understanding

Explanation

The problem is solved using Ohm's law, which is referenced in the provided context through the formula I=V/RI = V/R shown in the solution snippets. The potential difference VV is 12 V and the current II is given in milliamperes (mA), which must be converted to amperes (A) for the calculation. Rearranging the formula to R=V/IR = V/I allows for the calculation of the unknown resistance.

Solution Steps

  1. Given: Potential difference, V=12 VV = 12 \text{ V}; Current, I=2.5 mA=2.5×10−3 AI = 2.5 \text{ mA} = 2.5 \times 10^{-3} \text{ A}.

  2. Formula: From Ohm's law, we know that I=V/RI = V/R. Rearranging this to find resistance, we get R=V/IR = V/I.

  3. Calculation: R=12 V2.5×10−3 A=12×1032.5Ω=120002.5Ω=4800ΩR = \frac{12 \text{ V}}{2.5 \times 10^{-3} \text{ A}} = \frac{12 \times 10^3}{2.5} \Omega = \frac{12000}{2.5} \Omega = 4800 \Omega.

  4. Result: The value of the resistance of the resistor is 4800 Ω.

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