According to Joule's law of heating, heat produced H = I²Rt, where I is current, R is resistance and t is time. If the errors in the measurement of I, R and t are 3%, 4% and 6% respectively then error in the measurement of H is

To find the maximum error in the measurement of the heat produced, we use the formula for Joule's law of heating:
$H=I^{2}Rt$

According to the propagation of errors in multiplication and power terms, the fractional error in the calculated quantity $H$ is given by the sum of the fractional errors of the individual quantities multiplied by their respective powers (exponents):
$\frac{\Delta H}{H}=\pm \left(2\frac{\Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t}\right)$

To express this as percentage error, we multiply each term by 100%:
$\frac{\Delta H}{H}\times 100\%=\pm \left(2\left(\frac{\Delta I}{I}\times 100\%\right)+\left(\frac{\Delta R}{R}\times 100\%\right)+\left(\frac{\Delta t}{t}\times 100\%\right)\right)$

Given the percentage errors in the measurements:
Percentage error in current, $\frac{\Delta I}{I}\times 100\%=3\%$
Percentage error in resistance, $\frac{\Delta R}{R}\times 100\%=4\%$
Percentage error in time, $\frac{\Delta t}{t}\times 100\%=6\%$

Substituting these values into the error formula:
$\text{Percentage error in}H=\pm \left(2\times 3\%+4\%+6\%\right)$
$\text{Percentage error in}H=\pm \left(6\%+4\%+6\%\right)$
$\text{Percentage error in}H=\pm 16\%$

Thus, the correct answer is ±16%.