Principle of Galvanometer to Ammeter Conversion
A moving coil galvanometer is converted into an ammeter by connecting a low resistance, called the shunt resistance ($R_{sh}$), in parallel with the galvanometer. This allows the ammeter to measure larger currents.
Formula for Shunt Resistance
The relationship needed to calculate the shunt resistance is derived from the fact that the voltage across the galvanometer and the shunt must be equal:
\begin{equation*} I_g R_g = I_{sh} R_{sh} \end{equation*}
Where $I_{sh} = I - I_g$. Substituting this gives the standard formula:
\begin{equation*} R_{sh} = \frac{I_g R_g}{I - I_g} \end{equation*}
Here:
- $R_g$ is the resistance of the galvanometer coil.
- $I_g$ is the current required for full scale deflection of the galvanometer.
- $I$ is the total maximum current the ammeter needs to measure.
- $R_{sh}$ is the shunt resistance to be added in parallel.
Calculation for Correct Answer $0.5 \text{ }\Omega$
From the question, we have:
- Galvanometer resistance: $R_g = 100 \text{ }\Omega$
- Galvanometer full scale current: $I_g = 1 \text{ mA} = 1 \times 10^{-3} \text{ A}$
The expected answer is $0.5 \text{ }\Omega$ (Option D). Let's use the formula $R_{sh} = \frac{I_g R_g}{I - I_g}$ and solve for the total current $I$ that would yield this $R_{sh}$ value:
\begin{equation*} 0.5 \text{ }\Omega = \frac{(1 \text{ mA})(100 \text{ }\Omega)}{I - 1 \text{ mA}} \end{equation*}
Rearranging the formula to solve for $I$:
\begin{equation*} I - 1 \text{ mA} = \frac{(1 \text{ mA})(100 \text{ }\Omega)}{0.5 \text{ }\Omega} = \frac{100 \text{ mA}\Omega}{0.5 \text{ }\Omega} = 200 \text{ mA} \end{equation*}
\begin{equation*} I = 200 \text{ mA} + 1 \text{ mA} = 201 \text{ mA} \end{equation*}
This calculation implies that the intended full scale current range ($I$) for the ammeter is $201 \text{ mA}$ to achieve the answer $0.5 \text{ }\Omega$, rather than the $5 \text{ mA}$ stated in the question.
Verification
Using $I = 201 \text{ mA}$ and the given $I_g = 1 \text{ mA}$ and $R_g = 100 \text{ }\Omega$:
The current through the shunt would be $I_{sh} = I - I_g = 201 \text{ mA} - 1 \text{ mA} = 200 \text{ mA}$.
The shunt resistance is then:
\begin{equation*} R_{sh} = \frac{I_g R_g}{I_{sh}} = \frac{(1 \text{ mA})(100 \text{ }\Omega)}{200 \text{ mA}} = \frac{100 \text{ mA}\Omega}{200 \text{ mA}} = 0.5 \text{ }\Omega \end{equation*}
The required resistance is $0.5 \text{ }\Omega$.
Similar Questions
- The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
$E_y = 20 \sin(3 \times 10^6 x - 4.5 \times 10^{14} t) \text{ V/m}$
(where x, t and other values have S.I. units). The dielectric constant of the medium is _________.
(speed of light in free space is $3 \times 10^8 \text{ m/s}$) - A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $30^\circ$ from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is _________ mm.
$\left(\text{Take } \pi = \frac{22}{7}\right)$ - A cylindrical conductor of length 2 m and area of cross-section $0.2 \text{ mm}^2$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3} \text{ m}^2\text{/V.s}$. The value of $\alpha$ is :
(electron concentration $= 5 \times 10^{28} \text{/m}^3$ and electron charge = $1.6 \times 10^{-19} \text{ C}$) - A short bar magnet placed with its axis at $30^\circ$ with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \text{ J}$. The value of $\alpha$ is ______.
- A regular hexagon is formed by six wires each of resistance $r \text{ }\Omega$ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be
Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectric ($k_1$ and $k_2$) in the following fashion. Which of the following is true? ($k_1 > k_2$)
Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have common axis. The current through $P$ and $Q$ are $I$ and $4I$ respectively in clockwise direction as seen from $O$. The net magnetic field at $O$ is:
The reading of the ammeter ($A$) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is _______ A.
- A capacitor $C$ is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance $L$. In $t\text{ s}$ $25\%$ of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is __________ $\text{s}$.
The charge stored by the capacitor $C$ in the given circuit in the steady state is __________ $\mu\text{C}$.
Important Questions from Electricity and Magnetism
- The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
$E_y = 20 \sin(3 \times 10^6 x - 4.5 \times 10^{14} t) \text{ V/m}$
(where x, t and other values have S.I. units). The dielectric constant of the medium is _________.
(speed of light in free space is $3 \times 10^8 \text{ m/s}$) - A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $30^\circ$ from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is _________ mm.
$\left(\text{Take } \pi = \frac{22}{7}\right)$ - A cylindrical conductor of length 2 m and area of cross-section $0.2 \text{ mm}^2$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3} \text{ m}^2\text{/V.s}$. The value of $\alpha$ is :
(electron concentration $= 5 \times 10^{28} \text{/m}^3$ and electron charge = $1.6 \times 10^{-19} \text{ C}$) - A short bar magnet placed with its axis at $30^\circ$ with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \text{ J}$. The value of $\alpha$ is ______.
- A regular hexagon is formed by six wires each of resistance $r \text{ }\Omega$ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be
