Chapter 19, Problem 16P

To determine

The resistance of the resistor added in the circuit to for correcting the mistake and type of the connection.

Answer to Problem 16P

The resistor of resistance $960\Omega$ should be connected in parallel with wrong resistance soldered to fix the circuit without removing anything from existing circuit.

Explanation of Solution

Given info:

Actual resistance to be connected, $R_a=320\Omega$

Wrong resistance soldered in the circuit, $R_1=480\Omega$

Formula Used:

The resistance of the wrong resistor soldered is more than the actual resistance, so to fix this mistake connects another resistance in parallel with wrong resistance.

The expression to calculate the resistance to fix the existing circuit is,

  $R=\frac{R_1{R}_a}{R_1-R_a}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}R=\frac{\left(320\Omega \right)\left(480\Omega \right)}{480\Omega -320\Omega }\\ =960\Omega \end{array}$

Conclusion:

Therefore, the resistor of resistance $960\Omega$ should be connected in parallel with wrong resistance soldered to fix the circuit without removing anything from existing circuit.