Final answer:
To find the current through the primary winding of a transformer, we need to know the transformer turn ratio and apply the conservation of power for an ideal transformer, equating the power of the primary and secondary circuits (Pp = Ps). Without the transformation ratio, a numeric answer cannot be provided.
Step-by-step explanation:
To determine the current through the primary winding, we need to use the principle of conservation of energy in a transformer, assuming it is ideal and operates with 100% efficiency. By this assumption, the power in the primary (Pp) equals the power in the secondary (Ps), and for an ideal transformer, Pp = Ps. The power in an AC circuit is given by P = IV, where I is the current and V is the voltage. Therefore, if the secondary winding has a current of 0.5 A (assumed to be the rms current), and using the information from the challenge problem (ni-Cd batteries, step-down transformer, power in primary and secondary is 240 W), we can express the relationship between primary and secondary currents as Ip * Vp = Is * Vs.
Once we know the transformation ratio of the turns in the transformer, Np/Ns, and the voltage across the secondary coil, we can find the ratio of the primary and secondary currents. Assuming we have a transformation ratio (calculated from other given details), we can solve the equation Ip = (Ns/Np) * Is, where Is is the secondary current to find Ip, the primary current.
Without the specifics of the transformer's turn ratio, we cannot provide a numeric answer. The problem needs additional information from either a description of the transformer or from prior calculations or stated facts within the textbook or problem set.