Two resistors of 5 Ω and 10 Ω are connected in series in a circuit. The following options are possible:

(i) The potential difference across both resistors will be different.
(ii) The potential difference across both resistors will be the same.
(iii) The potential difference across the 5 Ω resistor will be twice that across the 10 Ω resistor.
(iv) The potential difference across the 10 Ω resistor will be twice that across the 5 Ω resistor.

Which of the above options are correct?

Correct option is C

The correct answer is option (C) (i) and (iv)

Explanation:

In a series circuit, the current is the same through all components, but the voltage is divided according to the resistances of the components. Since the resistance of the 10Ω resistor is twice that of the 5Ω resistor, the voltage drop across it will be twice as large. This gives us option (iv) as correct.

Option (i) is also correct because the voltage across each resistor will be different due to their different resistances.

Information Booster

• The current is the same across all resistors in a series circuit.

• The voltage drop is proportional to the resistance in a series circuit.

• The resistor with higher resistance will have a higher voltage drop.

• The total voltage across the series combination is the sum of the individual voltage drops.

• Ohm's law ($V=I\times R$) is used to calculate voltage drops.

Additional Knowledge

(i) The potential difference across both resistors will be different: In a series circuit, the voltage is divided across resistors according to their resistance. Since the resistors have different values, the voltage drops across them will be different.

(ii) The potential difference across both resistors will be the same: This is incorrect in a series circuit. The voltage drop across each resistor is proportional to its resistance.

(iii) The potential difference across the 5Ω resistor will be twice that across the 10Ω resistor: This is incorrect. The voltage across the 10Ω resistor will be twice that across the 5Ω resistor.

(iv) The potential difference across the 10Ω resistor will be twice that across the 5Ω resistor: This is correct. The voltage drop across the 10Ω resistor is twice that across the 5Ω resistor because its resistance is twice as large.