Solved: An ideal ammeter is modeled as a short circuit. A more realistic model of an

Chapter 5, Problem P5.5-10

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An ideal ammeter is modeled as a short circuit. A more realistic model of an ammeter is a small resistance. Figure P 5.5-10a shows a circuit with an ammeter that measures the current \(i_m\). In Figure P 5.5-10b, the ammeter is replaced by the model of an ideal ammeter, a short circuit. The ammeter measures \(i_{mi}\), the ideal value of \(i_m\).

As \(R_{\mathrm{m}} \rightarrow 0\), the ammeter becomes an ideal ammeter and \(i_{\mathrm{m}} \rightarrow i_{\mathrm{mi}}\). When \(R_{\mathrm{m}}>0\), the ammeter is not ideal and \(i_{\mathrm{m}}<i_{\mathrm{mi}}-\). The difference between \(i_{\mathrm{m}}\) and \(i_{\mathrm{mi}}\) is a measurement error caused by the fact that the ammeter is not ideal.

(a) Determine the value of \(i_{\mathrm{mi}}\).

(b) Express the measurement error that occurs when \(R_{\mathrm{m}}=\) \(20 \Omega\) as a percentage of \(i_{\mathrm{mi}}\).

(c) Determine the maximum value of \(R_{\mathrm{m}}\) required to ensure that the measurement error is smaller than 2 percent of \(i_{\mathrm{mi}}\).