Final answer:
To find the value of the resistor R in the circuit, use Ohm's law by applying it to the circuit on the right side of the figure with the equivalent resistor of 20. Divide the voltage across the circuit by the total resistance to find the current, and then use the current to calculate the resistance R.
Step-by-step explanation:
To find the value of the resistor R in the circuit, we need to use Ohm's law. Apply Ohm's law to the circuit on the right side of the figure with the equivalent resistor of 20. Ohm's law states that voltage (V) is equal to the product of current (I) and resistance (R): V = IR.
Since the current is the same in a series circuit, we can find the current by dividing the voltage across the circuit by the total resistance. Then, use the obtained current value to calculate the resistance R using Ohm's law.
For example, if the voltage across the circuit is 10 volts and the total resistance is 20 ohms, we can find the current by dividing 10 volts by 20 ohms, which gives 0.5 amps. Finally, we can find the value of the resistor R by dividing the voltage across resistor R by the current.