Current Electricity 2 Question 2

2. In the given circuit, an ideal voltmeter connected across the 10Ω resistance reads 2V. The internal resistance r, of each cell is

(2019 Main, 10 April I)

(a) 1.5Ω

(b) 0.5Ω

(c) 1Ω

(d) 0Ω

Show Answer

Solution:

  1. For the given circuit

Given,

VAB=2V

Current in circuit,

I=I1+I2=215+210[V=IR or I=V/R]=4+630=13A

Also, voltage drop across (r+r) resistors is

= voltage of the cell -voltage drop across AB

=32=1V

Using V=IR over the entire circuit

1=I(2+2r)=13(2+2r) [using Eq. (i)] 3=2+2r or 2r=1Ω or r=12Ω=0.5Ω

Alternative Solution

Equivalent resistance between A and B is

1RAB=110+115=16RAB=6Ω

Equivalent resistance of the entire circuit is, Req

=6Ω+2Ω+2r=8+2r

Now, current passing through the circuit is given as,

I=EnetR+req=EnetReq

where, R is external resistance, req is net internal resistance and Enet  is the emf of the cells.

 Here, Enet =1.5+1.5=3Vreq=r+r=2rI=38+2r

Also, reading of the voltmeter, V=2V=IRAB

2=38+2r×68+2r=9 or r=12=0.5Ω



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