Two resistances 60 pm 0.36 Omega and 30 pm 0 | vedclass

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(A) The equivalent resistance for two resistors in parallel is given by $R_P = \frac{R_1 R_2}{R_1 + R_2}$.Substituting the values: $R_P = \frac{60 	i

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$20 \pm 0.08 \ \Omega$

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(A) The equivalent resistance for two resistors in parallel is given by $R_P = \frac{R_1 R_2}{R_1 + R_2}$.Substituting the values: $R_P = \frac{60 	imes 30}{60 + 30} = \frac{1800}{90} = 20 \ \Omega$.To find the error $\Delta R_P$,we use the formula for parallel combination error:$\frac{\Delta R_P}{R_P^2} = \frac{\Delta R_1}{R_1^2} + \frac{\Delta R_2}{R_2^2}$.Alternatively,using logarithmic differentiation: $\Delta R_P = R_P \left( \frac{\Delta R_1}{R_1} + \frac{\Delta R_2}{R_2} - \frac{\Delta R_1 + \Delta R_2}{R_1 + R_2} ight)$.$\Delta R_P = 20 \left( \frac{0.36}{60} + \frac{0.09}{30} - \frac{0.36 + 0.09}{60 + 30} ight)$.$\Delta R_P = 20 \left( 0.006 + 0.003 - \frac{0.45}{90} ight)$.$\Delta R_P = 20 \left( 0.009 - 0.005 ight) = 20 	imes 0.004 = 0.08 \ \Omega$.Thus,the equivalent resistance is $20 \pm 0.08 \ \Omega$.

Two resistances $60 \pm 0.36 \ \Omega$ and $30 \pm 0.09 \ \Omega$ are connected in parallel. The equivalent resistance is

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