Question

If 12V is applied to a circuit containing a single 10kΩ 1/4W resistor, will it be safe to operate the circuit?

Answer 1

Yes, it is safe to operate the circuit, before the power dissipated is less than the maximum power

Explanation:

For a resistor, the power rating gives the maximum power at which the resistor is safe to operate.

For the resistor in this problem, this maximum power is given and it is

$P_{max}=\frac{1}{4}W=0.25 W$

The power dissipated on a resistor can be calculated with the equation

$P=\frac{V^2}{R}$

where

V is the potential difference applied on the resistor

R is the resistance

In this problem, we have:

$V=12 V\\R=10 k\Omega = 10,000 \Omega$

therefore, the power dissipated on the resistor is:

$P=\frac{12^2}{10,000}=0.014 W$

Which is less than the maximum power: therefore, yes, it will be safe to operate the circuit.

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