Final answer:
Increasing the current by 100% and reducing the resistance to 25% counterchecks each other effects, keeping the power dissipated the same according to the formula P = I^2 * R. Therefore, given the options, none is correct.
Step-by-step explanation:
The question involves the concept of power dissipation in a circuit, which is a topic covered in Physics. The power dissipated by a resistor can be calculated using the formula P = I^2 * R, where P is power, I is current, and R is resistance.
If the current through a resistance is increased by 100% (doubled), and simultaneously the resistance value is reduced to 25% (quartered), we would expect the power to change. According to the formula P = I^2 * R, when the current is doubled (I becomes 2I), the power is quadrupled (since P becomes (2I)^2 * R or 4I^2 * R). When the resistance R is reduced to 25% (R becomes 0.25R), the new power becomes 4I^2 * 0.25R, which is the original power P.
In conclusion, increasing the current by 100% and reducing the resistance to 25% keeps the power dissipated the same, which is not listed in the provided options; therefore, all the given options a) increased by 25%, b) increased by 50%, c) decreased by 25%, d) decreased by 50% are incorrect, assuming no typographical error in the question.