
Explain series connections of Resistors and derive the formula of equivalent resistance.
Answer
484.5k+ views
Hint: Resistor is an electrical component that is used to convert the current into the voltage or the voltage into the current. Resistors are said to be in series when they are connected in one line. Here, we will use ohm’s law to calculate the formula of equivalent resistance.
Complete step by step answer:
Consider a circuit carrying a current in which three resistors are connected in series. A voltage is connected to the circuit.
Here, , and are the resistors that are connected in series and , and are the voltage drops across the respective resistors.
Now, as the resistors are connected in series, the current flowing through the circuit will be the same across all the resistors. Now, the voltage across the circuit is given by
Now, if a resistor is placed in the place of these three resistors , and such that the current in the circuit remains the same, then is called the equivalent resistance.
Therefore, for an equivalent resistance, .
Now, the voltage drop across the resistance is .
The voltage drop across the resistance is .
The voltage drop across the resistance is .
Therefore, the voltage across the circuit is given by,
Now, taking common, we get
Now, as we know
Therefore,
Therefore, the above equation becomes
Which is the equivalent resistance.
Thus, we can say that the equivalent resistance in the circuit is the sum of all the individual resistances in the circuit.
Note:All the resistors in the series do not get a source voltage, therefore, they divide the voltage across them. Also, the amount of energy used by the resistors will be the same as the amount of energy used by a single resistor. This energy is also divided across the resistors depending upon their resistances.
Complete step by step answer:
Consider a circuit carrying a current

Here,
Now, as the resistors are connected in series, the current flowing through the circuit will be the same across all the resistors. Now, the voltage
Now, if a resistor

Therefore, for an equivalent resistance,
Now, the voltage drop across the resistance
The voltage drop across the resistance
The voltage drop across the resistance
Therefore, the voltage
Now, taking
Now, as we know
Therefore,
Therefore, the above equation becomes
Which is the equivalent resistance.
Thus, we can say that the equivalent resistance
Note:All the resistors in the series do not get a source voltage, therefore, they divide the voltage across them. Also, the amount of energy used by the resistors will be the same as the amount of energy used by a single resistor. This energy is also divided across the resistors depending upon their resistances.
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