3.2 A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

<p><strong>3.2 </strong>EMF of the battery = 10 V</p><p>Internal resistance of the battery, r = 3 Ω</p><p>Current in the circuit, I = 0.5 A</p><p>Let the resistance of the resistor be R</p><p>According to Ohm’s law</p><p>I =&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>E</mi></mrow></mrow><mrow><mrow><mo> (</mo><mi>R</mi><mo>+</mo><mi>r</mi><mo>)</mo></mrow></mrow></mfrac></math></span></p><p>R + r =&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>E</mi></mrow></mrow><mrow><mrow><mi>I</mi></mrow></mrow></mfrac></math></span>&nbsp;or R =&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>E</mi></mrow></mrow><mrow><mrow><mi>I</mi></mrow></mrow></mfrac></math></span>&nbsp;- r =&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>0.5</mn></mrow></mrow></mfrac></math></span>&nbsp;- 3 = 17 Ω</p><p>Terminal voltage of the battery when the circuit is closed is given by</p><p>V = IR = 0.5&nbsp;<span title="Click to copy mathml"><math><mo>×</mo><mn>17</mn><mo>=</mo><mn>8.5</mn><mi></mi><mi>V</mi></math></span></p><p>Therefore the resistance is 17 Ω and the terminal voltage is 8.5 V</p>

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