Intermittent windshield wipers use a variable resistor in an RC circuit to set the delay between successive passes of the wipers. A typical circuit is shown in Figure P23.76. When the switch closes, the capacitor (initially uncharged) begins to charge and the potential at point b begins to increase. A sensor measures the potential difference between points a and b, triggering a pass of the wipers when V_b = V_a. (Another part of the circuit, not shown, discharges the capacitor at this time so that the cycle can start again.) 

a. What value of the variable resistor will give 12 seconds from the start of a cycle to a pass of the wipers?

b. To decrease the time, should the variable resistance be increased or decreased?

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12 V Switch FIGURE P23.76 a 100 Ω Sensor • 47 ΚΩ Variable resistor b 100 μF