Three identical bulbs are connected as shown | vedclass

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

Question

(A) Let the resistance of each identical bulb be $R$. Case $1$: When switch $S$ is closed,bulbs $B$ and $C$ are in parallel,and this combination is in

Vedclass · Accepted Answer

$\frac{9 P}{4}$

Vedclass · Answer

(A) Let the resistance of each identical bulb be $R$. Case $1$: When switch $S$ is closed,bulbs $B$ and $C$ are in parallel,and this combination is in series with bulb $A$. The equivalent resistance is $R_{eq} = R + \frac{R \cdot R}{R + R} = R + \frac{R}{2} = \frac{3R}{2}$. The total current from the battery is $I = \frac{E}{R_{eq}} = \frac{2E}{3R}$. The voltage across the parallel combination of $B$ and $C$ is $V_{BC} = I \cdot \frac{R}{2} = \left(\frac{2E}{3R}\right) \cdot \frac{R}{2} = \frac{E}{3}$. The power consumed by bulb $B$ is $P = \frac{V_{BC}^2}{R} = \frac{(E/3)^2}{R} = \frac{E^2}{9R}$. Case $2$: When switch $S$ is opened,bulb $C$ is disconnected. Bulbs $A$ and $B$ are in series. The equivalent resistance is $R'_{eq} = R + R = 2R$. The current in the circuit is $I' = \frac{E}{2R}$. The power consumed by bulb $B$ is $P' = (I')^2 R = \left(\frac{E}{2R}\right)^2 R = \frac{E^2}{4R^2} \cdot R = \frac{E^2}{4R}$. Comparing $P$ and $P'$,we have $\frac{P'}{P} = \frac{E^2/4R}{E^2/9R} = \frac{9}{4}$. Therefore,$P' = \frac{9P}{4}$.

Three identical bulbs are connected as shown in the figure. When switch $S$ is closed,the power consumed in bulb $B$ is $P$. What will be the power consumed by the same bulb when switch $S$ is opened?

Similar Questions

$A$ $25\, W$,$220\, V$ bulb and a $100\, W$,$220\, V$ bulb are connected in series across a $220\, V$ line. Which electric bulb will glow more brightly?

$A$ storage battery of $emf$ $8.0\; V$ and internal resistance $0.5\; \Omega$ is being charged by a $120\; V$ $DC$ supply using a series resistor of $15.5\; \Omega$. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?

The current in the given circuit is ............ $A$.

In the adjoining circuit,the potential difference across $3\,\Omega$ is ................ $V$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module