Question

The PMMC ammeter A in the adjoining figure has a range of 0 to 3 mA. When switch $S_1$ is opened, the pointer of the ammeter swings to the 1 mA mark, returns and settles at 0.9 mA. The meter is

• A. critically damped and has a coil resistance of $100\Omega$
• B. Critically damped and has a coil resistance of $200\Omega$
• C. under damped and has a coil resistance of $100\Omega$
• D. under damped and has a coil resistance of $200\Omega$

Answer 1

The correct option is D under damped and has a coil resistance of $200\Omega$

Current through the PMMC ammeter is noted as 0.9 mA.

$0.9\times {10}^{-3}=\frac{1.8}{(1.8\times {10}^3+R_3)}$

$R_a=\text{ammeter resistance}$

$(0.9\times {10}^{-3})(1.8\times {10}^3+R_a)=1.8$

$0.9\times 1.8+0.9\times {10}^{-3}{R}_a=1.8$

$0.9\times {10}^{-3}{R}_a=1.8-0.9\times 1.8$

$0.9\times {10}^{-3}{R}_a=1.8\times 0.1$

$\therefore R_a=200\Omega$

Since, the points of the ammeter first swings around 1 mA and then settles at 0.9 mA, hence the ammeter is under-damped.