A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as shown in $\textbf{Fig. E29.20}$. Terminals $a$ and $b$ of winding $A$ may be connected to a battery through a reversing switch. State whether the induced current in the resistor $R$ is from left to right or from right to left in the following circumstances: (a) the current in winding $A$ is from $a$ to $b$ and is increasing; (b) the current in winding $A$ is from $b$ to $a$ and is decreasing; (c) the current in winding $A$ is from $b$ to $a$ and is increasing.