Final answer:
To find the voltage across the first capacitor, we must use the formula V = Q/C where V is the voltage, Q is the charge, and C is the capacitance. In a parallel circuit, each capacitor bears the full voltage of the battery. In a series circuit, the voltage divides between capacitors inversely proportional to their capacitances.
Step-by-step explanation:
To find the voltage Δv1 across the first capacitor, we need to understand the relationship between capacitance, charge, and voltage. The voltage V across a capacitor can be calculated using the formula V = Q/C, where Q is the charge and C is the capacitance.
In the context of a circuit with multiple capacitors in series or parallel, the total voltage in the circuit is the sum of the voltages across individual capacitors. If the capacitors are in parallel and connected to a voltage source like a battery, the voltage across each capacitor is equal to the voltage of the battery.
For instance, if we have three capacitors with capacitances C1, C2, and C3 connected in parallel to a 500-V battery, the voltage across each capacitor V1, V2, and V3, would be 500 V. The total charge on each capacitor would then be Q1 = C1*V1, Q2 = C2*V2, and Q3 = C3*V3 respectively.
If we are dealing with capacitors in series, the charge on each capacitor is the same, but the voltage divides based on the inverse of their capacitances. The expression for the voltage across capacitor 1 could be derived using V1 = Q/C1 where Q is the charge and C1 is the capacitance of the first capacitor.