The amount of heat produced in an electric circuit depends upon the current $(I),$ resistance $(R)$ and time $(t).$ If the error made in the measurements of the above quantities are $2\%, 1\%$ and $1\%$ respectively then the maximum possible error in the total heat produced will be $ ........... \%$
AIEEE 2012, Medium
Download our app for free and get started
Give $: \frac{\Delta I}{I} \times 100=2 \% ;$
$\frac{\Delta R}{R} \times 100=1 \% \text { and } \frac{\Delta t}{t} \times 100=1 \%$
Heat produced, $H=I^2 R t$
Maximum possible error in heat produced,
$=\frac{\Delta H}{H} \times 100$
$=2\left(\frac{\Delta I}{I} \times 100\right)+\frac{\Delta R}{R} \times 100+\frac{\Delta t}{t} \times 100$
$=2 \times 2 \%+1 \%+1 \%$
$=6 \%$
$\frac{\Delta R}{R} \times 100=1 \% \text { and } \frac{\Delta t}{t} \times 100=1 \%$
Heat produced, $H=I^2 R t$
Maximum possible error in heat produced,
$=\frac{\Delta H}{H} \times 100$
$=2\left(\frac{\Delta I}{I} \times 100\right)+\frac{\Delta R}{R} \times 100+\frac{\Delta t}{t} \times 100$
$=2 \times 2 \%+1 \%+1 \%$
$=6 \%$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionThe units of modulus of rigidity are
- 2If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as$ [\eta ^x \rho ^yr^z]$ where $\eta ,\rho $ and $r $ are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of $x, y$ and $z$ are given byView Solution
- 3A body travels uniformly a distance of $ (13.8 \pm 0.2)\,m$ in a time $(4.0 \pm 0.3)\, s$. The percentage error is ......... $\%$View Solution
- 4The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is ........ $\%$View Solution
- 5Pressure exerted by a gas is found to be $50\, N/m^2$ , then the value of pressure in $CGS$ system isView Solution
- 6View SolutionWhich of the following is not the unit of time
- 7If the error in the measurement of radius of a sphere is $2\%$ then the error in the determination of volume of the sphere will be ........ $\%$View Solution
- 8Using dimensional analysis, the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed asView Solution
- 9View SolutionWhich is not a unit of electric field
- 10View SolutionWhich of the following is dimensional formula for viscosity?