Final answer:
The current in a conducting loop with a given magnetic field, area, and resistance can be calculated using the formula I = B * A / R. In this case, the current is found to be 202.5 A.
Step-by-step explanation:
The current in a conducting loop can be calculated using the equation I = B * A / R, where I is the current, B is the magnetic field, A is the area of the loop, and R is the resistance of the loop.
In this case, the magnetic field is given by B = bt k, where b = 0.30 T/s. The area of the loop is 270 cm² and the resistance is 0.40 Ω.
Substituting these values into the equation, we have I = (0.30 * 270) / 0.40 = 202.5 A.
Therefore, the current in the conducting loop is 202.5 A.