Chapter 20, Problem 55P

To determine

The current for full scale deflection.

Answer to Problem 55P

The current for full scale deflection is $61.6\text{μA}$ .

Explanation of Solution

Given:

The current ( I ) through the galvanometer coil is $I=53\text{μA}$

Formula used:

The torque acting on it for full scale deflection is,

  $\tau =NABI$ .... (1)

Here, B is the magnetic field, n is the number of turns, and a is the area.

Calculation:

The torque acting on the coil for full scale deflection is denoted by $\tau$ .

Assume the magnetic field weaken to $B\text{'}=0.86B$ .

Show the expression for the torque acting on the coil for full scale deflection as follows:

  $\begin{array}{c}\tau =NA{B}^{\prime }{I}^{\prime }\\ =NA\left(0.86\right)I^{\prime }\\ =0.86NA{I}^{\prime }\end{array}$ .... (2)

Equate Equation (1) and (2).

  $\begin{array}{l}NABI=NA{B}^{\prime }{I}^{\prime }\\ BI=\left(0.86\right)I^{\prime }\\ I=0.86I^{\prime }\end{array}$

  $\begin{array}{l}{I}^{\prime }=1.163\left(53\mu A\right)\\ I^{\prime }=61.6\mu A\end{array}$

Conclusion:

Therefore, the current $\left(I^{\prime }\right)$ for full scale deflection is $61.6\text{μA}$ .