Final answer:
In a series circuit, the current through each resistor is the same. The equivalent resistor in the circuit would have the same resistance as the first resistor. Therefore, option E is true.
Step-by-step explanation:
In a series circuit, each resistor has the same amount of current flowing through it. Therefore, in the initial circuit where three resistors are connected in series, the current through each resistor (including the first resistor) would be equal. This means that option A is correct, the current through the equivalent resistor, R, equals the current through the first resistor, R1.
On the other hand, the voltage across each individual resistor in a series circuit is different. Therefore, the voltage across the equivalent resistor, R, would not be equal to the voltage across the first resistor, R1. So, option B is incorrect.
The power given off by a resistor is defined as the product of the voltage across it and the current flowing through it. Since the current through R is equal to the current through R1 (as explained above), and the voltage across R is not equal to the voltage across R1 (as explained above), option C is incorrect.
Based on the information above, the correct answer is option E. R, the equivalent resistor, is equal to R1.