Question

If the current I through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be

• A. 100%
• B. 200%
• C. 300%
• D. 400%

Answer 1

The correct option is C

300%

Step 1: Given

The current I through a resistor is increased by $100\%$

Step 2: Formula used

Power is calculated as the product of voltage and current, which can further lead to,

$P=I^{2}R[whereP=powerdissipiatedthrougharesistor,I=current,R=resis\tan ce]$

Step 3: Analyzing the increase in power dissipated

When the current through the resistor is increased by 100%, the new value of the circuit's current, indicated by I′, can be calculated as

$$\begin{gathered} I\text{'}=I+100\%ofI \\ I\text{'}=2I \end{gathered}$$

Then the power dissipated across the resistor can be calculated as

$$\begin{gathered} P\text{'}=I{\text{'}}^{2}R \\ SubstitutingI\text{'}=2I \\ P\text{'}=4I^{2}R \\ P\text{'}=4P \end{gathered}$$

When the current is increased by 100%, the power change is calculated as follows:

An increase in power dissipated is $\frac{P\text{'}-P}{P}\times 100$

Substituting $P\text{'}=4P$ in the increase in power dissipated

An increase in power dissipates is $\frac{4P-P}{P}\times 100=300\%$

As a result, boosting the current by 100% increases the power dissipated across the resistor by 300%.

Hence, option C is the correct answer