In a circuit there are two resistors of $3 Ω$ and an unknown resistor and they are connected in series across a $12 V$ battery. If the potential difference across the unknown resistor is $6 V$ then the equivalent resistance of the circuit is [[1]] $Ω$ .

Question

In a circuit there are two resistors of $3 Ω$ and an unknown resistor and they are connected in series across a $12 V$ battery. If the potential difference across the unknown resistor is $6 V$ then the equivalent resistance of the circuit is [[1]] $Ω$ .

Infinity Learn · Accepted Answer

If a circuit contains two resistors of 3 Ω each and an unknown resistor connected in series across a 12 V battery and the potential difference across the unknown resistor is 6 V then the equivalent resistance of the circuit is 12 Ω.It is given that two resistors, one of unknown resistance and the other of 3 Ω is connected in series combination across a 12 V battery.Let the potential difference across the 3 Ω resistance be V1. Therefore, the total resistance is equal to 12=6+V1+V1⇒ 6=2V1⇒V1=3VThe potential difference across the 3 Ω resistance is 3 V.Now, from the Ohm’s law, the current in the resistor 3 Ω is I=VR⇒I=33⇒ I=1 AHence, the current in the 3 Ω resistor is 1 A.Since all the resistors are connected in series connection, the current in the unknown resistor is also 1 A.The value of resistance such that the potential difference across the unknown resistor is 6 V and the current flowing through it is 1 A is R=VI⇒R=61⇒R=6 ΩSince the resistors are connected in series therefore equivalent resistance of the circuit id RS=3+3+6⇒RS=12 ΩHence, the equivalent resistance of the circuit is 12 Ω.

In a circuit there are two resistors of $3 Ω$ and an unknown resistor and they are connected in series across a $12 V$ battery. If the potential difference across the unknown resistor is $6 V$ then the equivalent resistance of the circuit is [[1]] $Ω$ .

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In a circuit there are two resistors of 3 Ω and an unknown resistor and they are connected in series across a 12 V battery. If the potential difference across the unknown resistor is 6 V then the equivalent resistance of the circuit is [[1]] Ω.

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Detailed Solution

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In a circuit there are two resistors of $3 Ω$ and an unknown resistor and they are connected in series across a $12 V$ battery. If the potential difference across the unknown resistor is $6 V$ then the equivalent resistance of the circuit is [[1]] $Ω$ .