Question

The energy dissipated by a resistor is $10mJ$ in $1s$ when an electric current of $2mA$ flows through it. The resistance is ________. (Round off to the nearest Integer)

Answer 1

Step 1: Given Data:

Dissipated energy is $H=10mJ=10\times {10}^{-3}J$

Time taken is $t=1s$

Current is $i=2mA$

Step 2: Formula Used:

Heat dissipated can be calculated as-

$H=i^{2}Rt$, where $R=$resistance, $H=$Heat, $i=$current and $t=$time

Step 3: Calculation of resistance

Using the formula of energy dissipated by a resistor can be calculated as-

$\begin{array}{rcl}H& =& i^{2}Rt\\ 10\times {10}^{-3}& =& {\left(2\times {10}^{-3}\right)}^2\times R\times 1\\ R& =& \frac{10\times {10}^{-3}}{{\left(2\times {10}^{-3}\right)}^2}\\ & =& 2500\Omega \end{array}$

The energy dissipated by a resistor is $10mJ$ in $1s$ when an electric current of $2mA$ flows through it. The resistance is$\begin{array}{r}2500\Omega \end{array}$.