Question

A voltmeter with resistance RVRVR_V is connected across the terminals of a battery of emf EEEMF and internal resistance rrr. Find the potential difference VmeterVmeterV_meter measured by the voltmeter.

Answer 1

Answer:

V = E - Ir

Explanation:

According to ohms law which states that the current I passing through a metallic conductor at constant temperature is directly proportional to the potential difference V across its ends. Mathematically,

V = IR... (1)

or E = IRt ... (2)

where;

V is the potential difference across the resistance R

E is the source voltage known as the electromotive force

I is the current

Rt is the effective resistance.

If a voltmeter with resistance Rohms is connected across emf E and internal resistance r, the external resistance and internal resistance will be in series with each other and their equivalent resistance Rt = R+r... (3)

Substituting equation 3 into equation 2 will give;

E = I(R+r)

E = IR+Ir ... (4)

Note that from equation 1, the potential difference V = IR

Substituting V = IR into equation 4 will result into;

E = V+Ir

V = E-Ir

The fore the potential difference V measured by the voltmeter is;

V = (E-Ir) meters

Answer 2

Answer:

Explanation:

Given:

Battery emf = E

Resistance of the voltmeter = R

Internal resistance = r

E = I× (R + r)

E = IR + Ir

Using ohms law,

Potential difference, V = IR

E = V + Ir

Making V the subject of formula,

V = E - Ir

Potential difference, V = E - Ir