Question

A 1000 V DC supply has two 1-core cables as its positive and negative leads: their insulation resistances to earth are $4M\Omega$ and$6M\Omega$, respectively, as shown in the figure. A voltmeter with resistance $50k\Omega$ is used to measure the insulation of the cable. When connected between the positive core and earth, then voltmeter reads

• A. 8 V
• B. 16 V
• C. 24 V
• D. 40 V

Answer 1

The correct option is A 8 V


Resistance of voltmeter $\left(R_v\right)$ appears parallel to 4$M\Omega .$

Effective resistance between A and B,
$R_{AB}=R_v||4M\Omega$

$R_v=50k\Omega =0.05M\Omega$

$R_{AB}=0.05||4M\Omega =0.05M\Omega$

$R_{AC}=R_{AB}+R_{BC}$

$=0.05+6=6.05M\Omega$

$I=\frac{1000}{R_{AC}}=\frac{1000}{6.05}\mu A$

Voltmeter reads,
$I{R}_{AB}=\frac{1000}{6.05}\times {10}^{-6}\times 0.05\times {10}^6\approx 8V$