Voltage and resistance for a resistor are measured as V = 200 ± 5 volts and R = 20 ± 0.2 Ω. The percentage error in current I = V/R is x. Find the value of 10x

The correct answer is 35.

To find the value of $10x$, where $x$ is the percentage error in the current $I$, we use the concept of propagation of errors in mathematical operations.
The relation between current ($I$), voltage ($V$), and resistance ($R$) is given by Ohm's law:
$I=\frac{V}{R}$

When a quantity is calculated as a quotient of two other quantities, the relative error in the calculated quantity is the sum of the relative errors of the individual quantities. Therefore, the relative error in current $I$ is:
$\frac{\Delta I}{I}=\frac{\Delta V}{V}+\frac{\Delta R}{R}$

We are given the following measured values with their corresponding absolute errors:
Voltage, $V=200\pm 5\text{V}$ (so $V=200$ and $\Delta V=5$)
Resistance, $R=20\pm 0.2\text{Ω}$ (so $R=20$ and $\Delta R=0.2$)

Now, let us calculate the relative error in current:
$\frac{\Delta I}{I}=\frac{5}{200}+\frac{0.2}{20}$

Let's simplify both terms on the right-hand side:
$\frac{5}{200}=0.025$
$\frac{0.2}{20}=0.01$

Adding these relative errors together, we get:
$\frac{\Delta I}{I}=0.025+0.01=0.035$

The percentage error in current $I$ (denoted by $x$) is the relative error multiplied by 100:
$x=\left(\frac{\Delta I}{I}\right)\times 100$
$x=0.035\times 100=3.5$

Finally, we calculate the value of $10x$:
$10x=10\times 3.5=35$