If the capacitance of a capacitor is doubled while keeping the charge constant,
Practice Questions
Q1
If the capacitance of a capacitor is doubled while keeping the charge constant, what happens to the potential difference across it? (2020)
It doubles
It halves
It remains the same
It quadruples
Questions & Step-by-Step Solutions
If the capacitance of a capacitor is doubled while keeping the charge constant, what happens to the potential difference across it? (2020)
Step 1: Understand the formula for capacitance, which is C = Q/V, where C is capacitance, Q is charge, and V is potential difference.
Step 2: Identify that in this scenario, the capacitance (C) is being doubled.
Step 3: Recognize that the charge (Q) remains constant throughout this process.
Step 4: Since C is doubled, we can write the new capacitance as 2C.
Step 5: Substitute the new capacitance into the formula: 2C = Q/V'. Here, V' is the new potential difference.
Step 6: Rearrange the equation to find V': V' = Q/(2C).
Step 7: Compare this with the original equation V = Q/C. Notice that V' is half of V.
Step 8: Conclude that if capacitance is doubled while keeping charge constant, the potential difference (V) must be halved.
Capacitance and Voltage Relationship – The relationship between capacitance (C), charge (Q), and potential difference (V) is defined by the formula C = Q/V, which shows how changes in capacitance affect voltage when charge is constant.
