The potential difference between positions (mathrm{a}) and (mathrm{b}) in Figure P31.51 is (6 mathrm{~V}), and (R_{1}=4.0 Omega,

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The potential difference between positions \(\mathrm{a}\) and \(\mathrm{b}\) in Figure P31.51 is \(6 \mathrm{~V}\), and \(R_{1}=4.0 \Omega, \mathscr{E}_{1}=10.0 \mathrm{~V}\), and \(\mathscr{E}_{2}=5.0 \mathrm{~V}\). What is the value of the resistance \(R_{2}\) ?

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