A series circuit contains five resistors. The total voltage applied to the circuit is 120 V. Four resistors have voltage drops of 35 V, 28 V, 22 V, and 15 V. What is the voltage drop of the fifth resistor?

To find the voltage drop across the fifth resistor in a series circuit, we can use the principle that the total voltage in a series circuit is equal to the sum of the voltage drops across each resistor. This is because in a series circuit, the current flowing through each component is the same and the total voltage across the circuit is the sum of the individual voltages across each component.

Let’s denote the voltage drop across the fifth resistor as V5. According to the problem, we know the following voltage drops across the four resistors: 35 V, 28 V, 22 V, and 15 V. The total voltage applied to the circuit is 120 V.

Now, we can sum up the known voltage drops and then subtract from the total voltage to find V5:

Total known voltage drops = 35 V + 28 V + 22 V + 15 V Total known voltage drops = 100 V

Now subtract the sum of the known voltage drops from the total voltage to find the voltage drop across the fifth resistor:

V5 = Total voltage - Total known voltage drops V5 = 120 V - 100 V V5 = 20 V

Therefore, the voltage drop across the fifth resistor is 20 V.

Extra: In the context of electrical circuits, a resistor is a component that resists the flow of electric current, causing a drop in voltage as the current passes through it. The voltage drop across a resistor in a series circuit depends on the resistor's resistance and the current flowing through the circuit. Ohm's law, which is V = IR (where V is the voltage, I is the current, and R is the resistance), describes this relationship.

For students learning about electricity, it's important to understand that series circuits have a single path for current to flow, which means that all components in a series circuit share the same current. Because of this, if you know the total voltage and the voltage drops across some of the components, you can always determine the remaining voltage drops as long as the total voltage and the individual voltage drops obey the principle of conservation of energy. This concept is crucial not only in basic electronics but also in understanding how various devices and systems are powered and how they operate.