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](https://tex.z-dn.net/?f=P_%7Bmax%7D%3D%5Cfrac%7B1%7D%7B4%7DW%3D0.25%20W)
The power dissipated on a resistor can be calculated with the equation
![P=\frac{V^2}{R}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BV%5E2%7D%7BR%7D)
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](https://tex.z-dn.net/?f=V%3D12%20V%5C%5CR%3D10%20k%5COmega%20%3D%2010%2C000%20%5COmega)
therefore, the power dissipated on the resistor is:
![P=\frac{12^2}{10,000}=0.014 W](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B12%5E2%7D%7B10%2C000%7D%3D0.014%20W)
Which is less than the maximum power: therefore, yes, it will be safe to operate the circuit.
Learn more about power and resistance:
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