Consider two identical galvanometers and two identical resistors with resistance R. If the...

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers

R_{c} < \frac{R}{2},

which of the following statement(s) about any one of the galvanometers
is(are) true ?

The maximum voltage range is obtained when all the components are connected in series

The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer

The maximum current range is obtained when all the components are connected in parallel

The maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors.

Solution:

i = \frac{E}{2 R + 2 R_{c}}

V_{g_{1}} = i R_{c} = \frac{E R_{c}}{2 (R + R_{c})} = \frac{E R_{c}}{2 R + 2 R_{c}}

i_{2} = \frac{E}{2 R + \frac{R_{c}}{2}}

V_{g_{2}} = \frac{i_{2}}{2} \times R_{c}

= \frac{1}{2} (\frac{E}{2 R + \frac{R_{c}}{2}}) \times R_{c}

V_{g_{2}} = \frac{E R_{c}}{4 R + R_{c}}

....(2)
Since

R_{c} < \frac{R}{2}

(2 R_{c} < R)

2 R + 2 R_{c} < 3 R

V_{g_{1}} > V_{g_{2}}

i_{A} = \frac{E}{R_{c}}

Here

i = \frac{E (2 R + 2 R_{c})}{2 R . 2 R_{c}} = \frac{E (R + R_{c})}{2 R R_{c}}

i_{B} = \frac{2 R}{2 R + 2 R_{c}} \times \frac{E (R + R_{c})}{2 R R_{c}} = \frac{E}{2 R_{c}}

i_{A} > i_{B}

Score

Ranking

Find Colleges

Compare Colleges

Exams

College Predictor

Course Finder

Your Gateway to Top Colleges & Exams

IIT Madras

IIT Delhi

IIT Bombay

IIT Kanpur

IIT Kharagpur

IIT Roorkee

IIT Guwahati

IIT Hyderabad

IIT BHU

IIT Dhanbad

IIT Indore

IIT Gandhinagar

IIT Ropar

IIT Jodhpur

IIT Mandi

IIT Patna

Top Exams

Consider two identical galvanometers and two identical resistors with resistance R. If the...

Ranking

Find Colleges

Compare Colleges

Exams

College Predictor

Course Finder

Your Gateway to Top Colleges & Exams

IIT Madras

IIT Delhi

IIT Bombay

IIT Kanpur

IIT Kharagpur

IIT Roorkee

IIT Guwahati

IIT Hyderabad

IIT BHU

IIT Dhanbad

IIT Indore

IIT Gandhinagar

IIT Ropar

IIT Jodhpur

IIT Mandi

IIT Patna

Top Exams

Consider two identical galvanometers and two identical resistors with resistance R. If the...

Join the conversation