Determine the magnitude of current I3. Let the voltage of the bottom battery VB =13.0 volts and r= 1.0 Ω.

To determine the magnitude of current I3, we need to consider the given voltage (VB = 13.0 volts) and resistance (r = 1.0 Ω). However, additional information is required to calculate the current.

To determine the current flowing through a resistance, we need to use Ohm's Law, which states that the current (I) flowing through a resistor is equal to the voltage across the resistor (V) divided by the resistance (R):

I = V / R

Since the given values pertain to "VB" and "r," it suggests that they correspond to the bottom battery and its internal resistance respectively. However, we need to know the connection of the battery with the rest of the circuit to determine the current.

Please provide more information about the circuit, such as the arrangement of the resistors and their values, or any additional voltages or currents given in the question.