Name: RC Circuit and Charging Capacitor
Uploaded: 2019-07-19
Duration: 13 min 36 s
Description: In this video, we will discuss the physics of charging the capacitor connected in a circuit and derive the expression and relation between the parameters inv...

Question

In the circuit shown below, $E_{1} = 3 V,$ $E_{2} = 2 V,$ $E_{3} = 1 V,$ and $R = r_{1} = r_{2} = r_{3} = 1 Ω$ . $(i)$ Find potential difference between the points $A$ and $B$ with $A & B$ disconnected.
$(ii)$ If $r_{2}$ is short-circuited and the point $A$ is connected to point $B$ by a zero resistance wire, find the current through $R$ .

Accepted Answer

(i) Since the three emfs are in parallel as given in the diagram then, the equivalent emf will be given as

$E_{eq} = \frac{(\frac{E_{1}}{r_{1}} + \frac{E_{2}}{r_{2}} + \frac{E_{3}}{r_{3}})}{(\frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}})}$ ,

Putting the values as given, we get,

$E_{eq} = \frac{(\frac{3}{1} + \frac{2}{1} + \frac{1}{1})}{(\frac{1}{1} + \frac{1}{1} + \frac{1}{1})} = 2 V$ ,

And, equivalent resistance is

$\frac{1}{R_{eq}} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1} = 3 \Rightarrow R_{eq} = \frac{1}{3} Ω$ ,

Now, if we draw an equivalent circuit diagram then, we get a circuit diagram as shown below,

Since, $A$ and $B$ are disconnected i.e; an open circuit. So, the current in the circuit will be $E_{2} = 2 V,$ then, we have,

$V_{A} - V_{B} = 2 - 0 = 2 V$

Hence, the potential difference between $A$ and $B$ is $2 V$ .

(ii) When $A$ is connected to $B$ with zero resistance wire and $r_{2}$ is short-circuited then, we get a circuit as shown below.

As $A$ is connected to $B$ with zero resistance wire so potential at $A & B$ will be equal to potential at $B$ , if we assume potential of $B = 0$ also $E_{2}$ has no internal resistance, so potential at $P$ will be $2 V$ , then, the potential difference between $A$ and $P$ will be $2 V$ ,

So, from Ohm's law, we can write,

$V_{A P} = I R (where, I is the current in resistor R) 2 = I \times 1 \Rightarrow I = 2 A$

Hence, the current in the resistor $R$ is $2 A$ .

Important Questions on Current Electricity

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In the circuit shown below, E1=3 V, E2=2 V, E3=1 V,and R=r1=r2=r3=1 Ω. (i) Find potential difference between the points A and B with A & B disconnected. (ii) If r2 is short-circuited and the point A is connected to point B by a zero resistance wire, find the current through R.

Important Questions on Current Electricity

Learn and Prepare for any exam you want !