Find the resistance of a wire in Ohms with the following conductance values: a) 0.006 S, b) 0.034 S, and c) 0.00202 S.
Understand the Problem
The question is asking us to calculate the resistance of a wire given its conductance. The relationship between resistance (R) and conductance (G) is inverse: R = 1/G. We need to apply this formula to each of the given conductance values (a, b, and c) to find the corresponding resistance in Ohms.
Answer
a) $50 \, \Omega$ b) $200 \, \Omega$ c) $1250 \, \Omega$
Answer for screen readers
a) $50 , \Omega$ b) $200 , \Omega$ c) $1250 , \Omega$
Steps to Solve
- State the formula relating Resistance and Conductance
Resistance ($R$) is the reciprocal of conductance ($G$). Therefore, the formula is:
$$ R = \frac{1}{G} $$
- Calculate Resistance for Conductance a
Given $G_a = 2 \times 10^{-2}$ Siemens, calculate $R_a$:
$$ R_a = \frac{1}{2 \times 10^{-2}} = \frac{1}{0.02} = 50 , \Omega $$
- Calculate Resistance for Conductance b
Given $G_b = 5 \times 10^{-3}$ Siemens, calculate $R_b$:
$$ R_b = \frac{1}{5 \times 10^{-3}} = \frac{1}{0.005} = 200 , \Omega $$
- Calculate Resistance for Conductance c
Given $G_c = 8 \times 10^{-4}$ Siemens, calculate $R_c$:
$$ R_c = \frac{1}{8 \times 10^{-4}} = \frac{1}{0.0008} = 1250 , \Omega $$
a) $50 , \Omega$ b) $200 , \Omega$ c) $1250 , \Omega$
More Information
The unit of resistance, $\Omega$ (Ohms), is the reciprocal of the unit of conductance, S (Siemens). This inverse relationship simplifies calculations when conductance is known and resistance needs to be determined, or vice versa.
Tips
A common mistake is to incorrectly manipulate the scientific notation when calculating the reciprocal. For example, incorrectly calculating $1/(2 \times 10^{-2})$ as $0.5 \times 10^{-2}$ instead of $0.5 \times 10^{2} = 50$. Pay close attention to the negative exponents.
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