Find V_A - V_B for the following given circui | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) In the steady state, the capacitors act as open circuits. The current $I$ flows through the outer loop containing the $24 	ext{ V}$ battery and t

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(D) In the steady state, the capacitors act as open circuits. The current $I$ flows through the outer loop containing the $24 	ext{ V}$ battery and the $2 	ext{ }\Omega$ resistor in series with the parallel combination of the $(4 	ext{ }\Omega + 6 	ext{ }\Omega)$ resistor branch.First, calculate the total resistance of the circuit:$R_{eq} = 2 + (4 + 6) = 2 + 10 = 12 	ext{ }\Omega$.The current in the circuit is:$I = \frac{V}{R_{eq}} = \frac{24}{12} = 2 	ext{ A}$.The voltage across the parallel branch (between points $x$ and $y$) is:$V_{xy} = I 	imes (4 + 6) = 2 	imes 10 = 20 	ext{ V}$.Now, consider the capacitor branch. The capacitors $C_1 = 4/3 	ext{ }\mu	ext{F}$ and $C_2 = 4 	ext{ }\mu	ext{F}$ are in series across the $20 	ext{ V}$ potential difference.The equivalent capacitance is $C_{eq} = \frac{C_1 C_2}{C_1 + C_2} = \frac{(4/3) 	imes 4}{(4/3) + 4} = \frac{16/3}{16/3} = 1 	ext{ }\mu	ext{F}$.The charge on the capacitors is $Q = C_{eq} V_{xy} = 1 	ext{ }\mu	ext{F} 	imes 20 	ext{ V} = 20 	ext{ }\mu	ext{C}$.The potential difference across the $4 	ext{ }\mu	ext{F}$ capacitor is:$V_{C2} = \frac{Q}{C_2} = \frac{20 	ext{ }\mu	ext{C}}{4 	ext{ }\mu	ext{F}} = 5 	ext{ V}$.The potential difference across the $4 	ext{ }\Omega$ resistor is $V_{yB} = I 	imes 4 = 2 	imes 4 = 8 	ext{ V}$.Using the potential path from $B$ to $A$:$V_B + 8 - V_{C1} - V_A = 0$ (where $V_{C1} = 20 - 5 = 15 	ext{ V}$).Alternatively, $V_A - V_B = V_{xy} - V_{C2} - V_{x B} = 20 - 5 - (2 	imes 6) = 20 - 5 - 12 = 3 	ext{ V}$.Wait, re-evaluating the path: $V_A - V_B = (V_A - V_y) - (V_B - V_y) = 15 - 8 = 7 	ext{ V}$.

Find $V_A - V_B$ for the following given circuit in volts.

Similar Questions

Five identical capacitors, each of capacitance $20 \mu F$, are connected to a battery of $150 V$ in the combination shown in the diagram. What is the total amount of charge stored?

The potential difference that must be applied across the series and parallel combination of $4$ identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is

The potential difference that must be applied across the parallel and series combination of three identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is

The numerical value of the charge on either plate of the capacitor $C$ shown in the figure is

$A$ metal sphere of radius $1 \ m$ is charged with $10^{-2} \ C$ in air. Its bulk modulus is $10^{11} / 4 \pi^{2} \ N/m^2$. The volume strain in the sphere is $(\epsilon_{0} = \text{permittivity of free space})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module