Question

A voltmeter and a ammeter are connected in series to an ideal cell of emf E. The voltmeter reading is V, and the ammeter reading is I. Then
a. V < E
b. The voltmeter resistance is V/I
c. The potential difference across the ammeter is E-V
d. Voltmeter resistance + ammeter resistance = E/I

Correct statements are
A. i and ii
B. ii and iii
C. iii and iv
D. all

Answer 1

Hint To find the given values we have to treat all the voltmeters and ammeters as a set of resistances. Then we have to obtain voltage differences and current across each section.

Complete step-by-step solution :
(i) The reading of voltmeter V: $V = E - {V_A}$
$V < E$
(ii) Resistance of voltmeter V: ${R_V} = V/I$
(This equation is derived by the ohm’s law)
(iii) Potential difference across ammeter A: ${V_A} = E - V$
(iv) Total resistance of the circuit:

${R_T} = {R_V} + {R_A}$

As the total resistance would be the series sum of the resistances along the voltmeter and ammeter.
Also from ohm's law, total resistance of the circuit
${R_T} = E/I$
${R_V} + {R_A} = E/I$
Therefore all the given statements are correct. Hence the correct option will be option D.

Note:- All the ammeter and voltmeters are considered as ideal in this case. They are treated as ideal resistance in deriving the equations.