At a place, the horizontal and vertical components of Earth's magnetic field are of 0.4 and 0.3 unit. The total intensity of Earth's magnetic field is a. 0.7 unit b. 0.5 unit c. 0.4 unit d. 0.3 unit

Step 1: Apply Ohm's law to find the current through the resistor $I_R$$I_R=\frac{V}{H}$ Step 2: Substitute the given values of voltage and hypotenuse $I_R=\frac{0.3}{0.4}$ Step 3: Simplify the expression $I_R=0.75$ Step 4: Calculate the square of the current through the resistor $I_R^2={\left(0.75\right)}^2=0.5625$ Step 5: Use the Pythagorean theorem to find the square of the hypotenuse $H^2=V^2+I_R^2$ Step 6: Substitute the values of voltage and the square of the current through the resistor $H^2={\left(0.3\right)}^2+0.5625$ Step 7: Simplify the expression $H^2=0.09+0.5625=0.6525$ Step 8: Take the square root of both sides to find the value of the hypotenuse $H=\sqrt{0.6525}$ Step 9: Round the answer to the appropriate number of significant figures $H=0.81$ Step 10: Calculate the current through the resistor using the hypotenuse and voltage $I_R=\frac{V}{H}=\frac{0.3}{0.81}$ Step 11: Simplify the expression $I_R=0.37$ Step 12: Calculate the square of the current through the resistor $I_R^2={\left(0.37\right)}^2=0.1369$ Step 13: Use the Pythagorean theorem to find the square of the hypotenuse $H^2=V^2+I_R^2$ Step 14: Substitute the values of voltage and the square of the current through the resistor $H^2={\left(0.3\right)}^2+0.1369$ Step 15: Simplify the expression $H^2=0.09+0.1369=0.2269$ Step 16: Take the square root of both sides to find the value of the hypotenuse $H=\sqrt{0.2269}$ Step 17: Round the answer to the appropriate number of significant figures $H=0.48$ Step 18: Calculate the current through the resistor using the hypotenuse and voltage $I_R=\frac{V}{H}=\frac{0.3}{0.48}$ Step 19: Simplify the expression $I_R=0.625$ Step 20: Calculate the square of the current through the resistor $I_R^2={\left(0.625\right)}^2=0.390625$ Step 21: Use the Pythagorean theorem to find the square of the hypotenuse $H^2=V^2+I_R^2$ Step 22: Substitute the